Hypothesis Testing for Population Proportions, Exercises of Statistics

Download Hypothesis Testing for Population Proportions and more Exercises Statistics in PDF only on Docsity! lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804  Steve listens to his favorite streaming music service when he works out. He wonders whether the service algorithm does a good job of finding random songs that he will like often. To test this, he listens to 50 songs chosen by the service at random and finds that he likes 32 of them. Use Excel to test whether Steve will like a randomly selected song more than not and then draw a conclusion in the context of a problem. Use α = 0.05. Type equation here . Ho: p = ≤ 0.5 (50%) p = 0.5 Ha: p = > 0.5 (strictly ¿>≠ ) P-value = 0.02 which is < α =0.05 we reject Ho and support the Ha Hypothesis Test for p population proportion Level of Significance Proportion under (decimal) (decimal) H0 n Number of Successes Sample Proportion StDev SE Test Statistic (z) One-Sided p-value Two-Sided p-value Right-Tailed (>) Left-Tailed (<) Two-Tailed (≠) ± 0.05 0.5000 50 32 0.640000 0.500000 0.070711 1.979899 0.023852 0.047704 1.644854 - 1.644854 1.959964 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Answer: Reject the null hypothesis. There is sufficient evidence to prove that Steve will like a random selected song more often than not.  A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested 2 types of batteries and claimed that the batteries from company A outperformed batteries from company B in 108 of the tests. There were 200 tests. Company B decided to sue the magazine, claiming that the results were not significantly different from 50% and that the magazine was slandering its good name. Use Excel to test whether the true proportion of times that Company A’s batteries outperformed Company B’s batteries is different from 0.5. Identify the p=value rounding it to 3 decimal places. Ho: p = 0.5 Ha ≠ 0.5 (two tailed test) n = 200 (α is not given soleave it 0.05) Hypothesis Test for p population proportion Level of Significance Proportion under H0 n Number of Successes Sample Proportion StDev SE Test Statistic (z) One-Sided p-value Two-Sided p-value Right-Tailed (>) Left-Tailed (<) Two-Tailed (≠) ± Answer: 0.258 (because it is a two tailed test). We are not rejecting the null hypothesis and we do not have evidence to support the alternative hypothesis.  A candidate in an election lost by 5.8% of the vote. The candidate sued the state and said that more than 5.8% of the ballots were defective and not counted by the voting machine, so a full recount would need to be done. His opponent wanted to ask for the case to be dismissed, MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 0.05 0.5000 200 108 0.540000 0.500000 0.035355 1.131371 0.129238 0.258476 1.644854 - 1.644854 1.959964 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Hypothesis Test for p population proportion Level of Significance Proportion under H0 n Number of Successes Sample Proportion StDev SE Test Statistic (z) One-Sided p- value Two-Sided p- value Answer: 0.048  An economist claims that the proportion of people that plan to purchase a fully electric vehicle as their next car is greater than 65%. To test this claim, a random sample of 750 people were asked if they planned to purchase a fully electric vehicle as their next car. Of this 750, 513 indicated that they plan to purchase an electric vehicle. Ho: p = 0.65 Ha; p = >0.65 Find the p-value for this hypothesis test for a proportion & round to 3 decimal places. Hypothesis Test for p population proportion MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 0.050 0 0.0 5 1500 61 0.04066 7 0.21794 5 0.00562 7 - 1.65857 7 0.04845 7 0.09691 4 0.025588 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Level of Significance Proportion under H0 n Number of Successes Sample Proportion StDev SE Test Statistic (z) One-Sided p-value Two-Sided p-value Answer: 0.026  Colton makes the claim to his classmates that < 50% of newborn babies born this year in his state are boys. To prove this claim, he selects a random sample of 344 birth records in his state from this year. Colton found that 176 of the newborns were boys. What are the null and alternative hypothesis for this hypothesis test. Answer: Ho: 0.5 Ha: <0.5  An Airline company claims that in its recent advertisement that at least 94% of passenger luggage that is lost is recovered and reunited with their customer within 1 day. Hunter is a graduate student studying statistics. For a research project, Hunter wants to find out whether there is sufficient evidence in support of the airline company’s claim. He randomly selects 315 passengers whose luggage was lost by the airlines and found out that 276 of those passengers were reunited with their luggage within 1 day. Are all of the conditions for his hypotheses test met, and if so, what are the Ho and Ha for this hypothesis test? For a binomial Model to follow the normal model, the following condition must be satisfied: Success count = n * p ≥ 5 and Failure count ≥5 Example: success count 315 * 0.94 = 296.1 and failure count 315-296.1 = 18.9 so it meets the conditions. Answer: All of the conditions were met and the Ho = 0.94; Ha = >0.94 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 0.05 0.6500 750 513 0.684000 0.476970 0.017416 1.952175 0.051176 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+  A college administrator claims that the proportion of students who are nursing majors is > 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors. The following is the set up for the hypothesis test: Ho: p = . 40 and Ha: p = >.40 Find the test statistics for this hypothesis test for a proportion & round to 2 decimal places. Answer: 3.06 Level of Significance Proportion under H0 n Number of Successes Sample Proportion MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 0.475000 0.05 0.4000 400 190 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+  Marty, a typist, claims his average typing speed is 72 wpm. During a practice session, Marty has a sample typing speed mean of 84 wpm based on 12 trials. At the 5% significance level, does the data provide sufficient evidence to conclude that his mean typing speed is >72 wpm? Accept or reject the hypothesis given the data below. Ho: μ=72 wpm ; Ha: μ=¿ 72 wpm ; α =0.05 ( significance level ) ; Zo = 2.1; p = 0.018 Answer: Reject the null hypothesis because the p-value 0.018 is less than the significance level α =0.05  What is the p-value of a right-tailed one mean hypothesis test, with a test statistic of Zo = 2.1? (Do not round your answer. Compute your answer using a value from the table. (Value in table was 0.982) 1 – 0.982 = p=value of 0.018 Answer: 0.018  What is the p-value of a two-tailed one mean hypothesis test, with a test statistic of Zo = 0.27? (Do not round your answer. Compute your answer using a value from the table. (Value in table was 0.606) 1-0.606 = P-value of 0.394 because it is two tailed, you multiply 2 x .394 = .788 Answer: 0.788  Raymond, a typist, claims his average typing speed is 89 wmp. During a practice session, Raymond has a sample typing speed mean of 95.5 wmp based on 15 trials. At the 1% significance level, does the data provide sufficient evidence to conclude that his mean typing speed is > 89 wmp? Accept or reject the hypothesis given the sample data below: Ho: μ=89 ; Ha: μ=¿ 89 wmp α =0.02 Sig Level; Zo = 2.75; p = 0.003 Answer: Reject the null hypothesis because p-value 0.003 is less than alpha 0.02  Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000 per year. Gina, his colleague, believes this to be incorrect, so she randomly selects 61 employees who work in Yarmouth and record their annual salary. Gina calculates the sample mean income to be $56.500 per year with a sample standard deviation of $3750. Using the alternative hypothesis, Ha = μ=¿ $ 55,000 , find the test statistic τ and the p-value for the appropriate hypothesis test. Round the τ to 2 decimal places and the p-value to 3 decimal places. Hypothesis Test for µ for unknown population stdev MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Level of Significance Mean under H0 n Sample Mean StDev (decimal) MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 0.1 55000 61 56500 3750 Week lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ SE Test statistic (t) One- Sided p- value Two-Sided p- value Answer: t = 3.12; p-value = 0.001  A college administrator claims that the proportion of students that are nursing majors is less than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 149 are nursing majors. The following is the setup for this hypothesis test: H0:p=0.40 Ha:p<0.40 Find the p-value for this hypothesis test and round your answer to 3 decimal places. Hypothesis Test for p population proportion Level of Significance Proportion under H0 n Number of Successes Sample Proportion StDev SE Test Statistic (z) One-Sided p- MATH 225N Hypothesis Testing Question and Answers 480.13830 0 3.124100 0.001373 0.002746 0.05 0.4000 400 149 0.024495 - 1.122683 0.131357 0.262714 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+  A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4000 people are checked and 170 are determined to have the cancer. The following is the setup for this hypothesis test: H0:p=0.05 Ha:p<0.05 In this example, the p-value was determined to be 0.015. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Select the correct answer below: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. (p=0.015 α =0.05 ¿ The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim. (So, if p≤α, reject H0; otherwise fail to reject H0)  A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts. The following is the setup for this hypothesis test: H0:p=0.65 Ha:p<0.65 In this example, the p-value was determined to be 0.277. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Select the correct answer below: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim.  A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime. The following is the setup for this hypothesis test: H0:p = 0.35 Ha:p ≠ 0.35 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. Provide your answer below: 0.075  A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200 random students and determines that 151 students pass the exam. The following is the setup for this hypothesis test: H0:p=0.80 Ha:p>0.80 In this example, the p-value was determined to be 0.944. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Sample Proportion StDev SE Test Statistic (z) One-Sided p- MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 0.661667 0.458258 0.018708 - 2.049003 0.020182 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ value Two-Sided p- value  Kathryn, a golfer, has a sample driving distance mean of 187.3 yards from 13 drives. Kathryn still claims that her average driving distance is 207 yards, and the low average can be attributed to chance. At the 1% significance level, does the data provide sufficient evidence to conclude that Kathryn's mean driving distance is less than 207 yards? Given the sample data below, accept or reject the hypothesis. • H0:μ=207 yards; Ha:μ<207 yards • α=0.01 (significance level) • z0=−1.46 • p=0.0721 Select the correct answer below: Reject the null hypothesis because the p-value 0.0721 is greater than the significance level α=0.01. Do not reject the null hypothesis because the p-value 0.0721 is greater than the significance level α=0.01. Reject the null hypothesis because |−1.46|>0.01. Do not reject the null hypothesis because |−1.46|>0.01. Do not reject the null hypothesis because the value of z is negative.  Mary, a javelin thrower, claims that her average throw is 61 meters. During a practice session, Mary has a sample throw mean of 55.5 meters based on 12 throws. At the 1% significance level, does the data provide sufficient evidence to conclude that Mary's mean throw is less than 61 meters? Accept or reject the hypothesis given the sample data below. • H0:μ=61 meters; Ha:μ<61 meters • α=0.01 (significance level) • z0=−1.99 • p=0.0233 Select the correct answer below: Reject the null hypothesis because |−1.99|>0.01. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 0.04036 4 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Do not reject the null hypothesis because |−1.99|>0.01. Reject the null hypothesis because the p-value 0.0233 is greater than the significance level α=0.01. Do not reject the null hypothesis because the value of z is negative. Do not reject the null hypothesis because the p-value 0.0233 is greater than the significance level α=0.01.  Elizabeth claims that her average typing speed is at least 87 words per minute MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ • H0:μ=140; Ha:μ<140 • α=0.05 (significance level) • z0=−0.52 • p=0.3015 Select the correct answer below: Reject the null hypothesis because the value of z is negative. Do not reject the null hypothesis because |−0.52|>0.05. Reject the null hypothesis because the p-value 0.3015 is greater than the significance level α=0.05. Do not reject the null hypothesis because the p-value 0.3015 is greater than the significance level α=0.05. Reject the null hypothesis because |−0.52|>0.05.  Timothy, a bowler, has a sample game score mean of 202.1 from 11 games. Timothy still claims that his average game score is 182, and the high average can be attributed to chance. At the 5% significance level, does the data provide sufficient evidence to conclude that Timothy's mean game score is greater than 182? Given the sample data below, accept or reject the hypothesis. • H0:μ=182; Ha:μ>182 • α=0.05 (significance level) • z0=1.57 • p=0.0582 Select the correct answer below: Reject the null hypothesis because the p-value 0.0582 is greater than the significance level α=0.05. Do not reject the null hypothesis because the p-value 0.0582 is greater than the significance level α=0.05. Do not reject the null hypothesis because 1.57>0.05. Reject the null hypothesis because the value of z is positive. Reject the null hypothesis because 1.57>0.05.  What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−1.59? (Do not round your answer; compute your answer using a value from the table below.) Table score was 0.056. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Provide your answer below: .112 31. What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=2.05? (Do not round your answer; compute your answer using a value from the table below.) The number on the table was .980 1-.980 = .02 Answer: 0.02 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 30. What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−1.19? Use a p-value rounded to 3 decimal places. P = 0.117 31. What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−0.65? (Do not round your answer; compute your answer using a value from the table below. Answer: 0.258 32. What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=0.36? (Do not round your answer; compute your answer using a value from the table below.) Number in table .641 1 – 0.641 = .359 Answer: 0.359 33. What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=1.82? (Do not round your answer; compute your answer using a value from the table below.) Number in table was 0.966. So 1-.966 = 0.034 Answer: 0.034 34. What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−1.73? (Do not round your answer; compute your answer using a value from the table below.) Table # was 0.042 so 0.042 * 2 = 0.084 Answer: 0.084 35. A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20% of the complaints should have been filed on Monday. She randomly selected 50 complaints and checked the day that they were submitted. In those complaints 13 were submitted on a Monday. The CEO conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of complaints submitted on a Monday is different from 20%. lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 37. A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20% of the complaints should have been filed on Monday. She randomly selected 50 complaints and checked the day that they were submitted. In those complaints 13 were submitted on a Monday. The CEO conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of complaints submitted on a Monday is different from 20%. (a) H0:p=0.2; Ha:p≠0.2, which is a two-tailed test. (b) Use Excel to test whether the true proportion of complaints submitted on a Monday is different from 20%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places. Answer: t = 1.061 p = 0.289 Hypothesis Test for p population proportion Level of Significance Proportion under H0 n Number of Successes Sample Proportion StDev SE Test Statistic (z) One-Sided p-value Two-Sided p-value 38. A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20% of the complaints MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 0.05 0.2000 50 13 0.260000 0.400000 0.056569 1.060660 0.144572 0.289144 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ should have been filed on Monday. She randomly selected 50 complaints and checked the day that they were submitted. In those complaints 13 were submitted on a Monday. The CEO conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of complaints submitted on a Monday is different from 20%. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ (a) H0:p=0.2; Ha:p≠0.2, which is a two-tailed test. (b) z0=1.061, p-value is = 0.289 (c) Which of the following are appropriate conclusions for this hypothesis test? Select all that apply. Select all that apply: • We reject H0. • We fail to reject H0. • At the 5% significance level, the data provide sufficient evidence to conclude the true proportion is different than 20%. • At the 5% significance level, the data do not provide sufficient evidence to conclude the true proportion is different than 20%. 39. A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250 orders and determines that 60 orders are take out orders. The following is the setup for this hypothesis test: • {H0:p=0.25Ha:p>0.25 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Hypothesis Test for p population proportion Level of Significance Proportion under H0 n Number of Successes MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 0.05 0.2500 250 60 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 42. The owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. Specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. Chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. She randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. What are the null and alternative hypotheses for this hypothesis test? MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Select the correct answer below: H0:p=0.63 Ha:p>0.63 H0:p=0.63 Ha:p<0.63 H0:p≠0.63 Ha:p=0.63 H0:p=0.63 Ha:p≠0.63 43. A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%. To test this claim, a survey asked 500 randomly selected college students if they planned to perform community service after graduation. Of those students, 195 indicated they planned to perform community service. The following is the setup for the hypothesis test: H0:p=0.35 Ha:p>0.35 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Provide your answer below: T = 1.88 44. A researcher claims that the proportion of people over 65 years of age in a certain city is greater than 11%. To test this claim, a sample of 1000 people are taken and its determine that 126 people are over 65 years of age. The following is the setup for this hypothesis test: {H0:p=0.11 Ha:p>0.11 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Hypothesis Test for p population proportion MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 46. Which of the following results in a null hypothesis p≤0.61 and alternative hypothesis p>0.61? Select the correct answer below: A study says that at least 61% of students study less than 5 hours per week. A researcher thinks this is incorrect, and wants to show that fewer than 61% of students study less than 5 hours per week. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ A study says that more than 61% of students study less than 5 hours per week. A researcher thinks this is incorrect, and wants to show that at least 61% of students study less than 5 hours per week. A study says that at most 61% of students study less than 5 hours per week. A researcher thinks this is incorrect, and wants to show that more than 61% of students study less than 5 hours per week. A study says that less than 61% of students study less than 5 hours per week. A researcher thinks this is incorrect, and wants to show that more than 61% of students study less than 5 hours per week. 47. Suppose the null hypothesis, H0, is: a weightlifting bar can withstand weights of 800 pounds and less. What is α, the probability of a Type I error in this scenario? the probability that you think the weightlifting bar can withstand weights of 800 pounds and less when, in fact, it cannot the probability that you think the weightlifting bar can withstand weights of 800 pounds and less when, in fact, it can the probability that you think the weightlifting bar cannot withstand weights of 800 pounds and less when, in fact, it can the probability that you think the weightlifting bar cannot withstand weights of 800 pounds and less when, in fact, it cannot 48. Suppose a pitcher claims that his pitch speed is less than 43 miles per hour, on average. Several of his teammates do not believe him, so the pitcher decides to do a hypothesis test, at a 10% significance level, to persuade them. He throws 19pitches. The mean speed of the sample pitches is 35 miles per hour. The pitcher knows from experience that the standard deviation for his pitch speed is 6 miles per hour. • H0: μ≥43; Ha: μ<43 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Hypothesis Test for µ Population stdev known Level of Significance MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 0.01 lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Mean under H0 43 n 19 Sample Mean 35 StDev 6 SE 1.376494 Test Statistic (z- -5.811865 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Which graph below corresponds to the following hypothesis test? H0:X=14.7, Ha:X≠14.7 Select the correct answer below: 52. Determine the Type I error if the null hypothesis, H0, is: an electrician claims that no more than 10% of homes in the city are not up to the current electric codes. Select the correct answer below: The electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, there really are no more than 10% that are not up to the current electric codes. The electrician thinks that more than 10% of the homes in the city are not up to the current electrical codes when, in fact, there really are more than 10% of the homes that do not meet the current electric codes. The electrician thinks that more than 10% of the homes in the city are not up to the current electrical codes when, in fact, at most 10% of the homes in the city are not up to the current electric codes. The electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, more than 10% of the homes are not up to the current electric codes. 53. Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 years. What is the Type I error in this scenario? Select the correct answer below: MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ You think the mean age of the horses on a ranch is 6 years when, in fact, it is. You think the mean age of the horses on a ranch is 6 years when, in fact, it is not. You think the mean age of the horses is not 6 years when, in fact, it is. You think the mean age of the horses is not 6 years when, in fact, it is not. 54. What is β, the probability of a Type II error if the null hypothesis, H0, is: an electrician claims that no more than 10% of homes in the city are not up to the current electric codes. Select the correct answer below: MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ the probability that the electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, there really are no more than 10% that are not up to the current electric codes the probability that the electrician thinks that more than 10% of the homes in the city are not up to the current electrical codes when, in fact, there really are more than 10% of the homes that do not meet the current electric codes the probability that the electrician thinks that more than 10% of the homes in the city are not up to the current electrical codes when, in fact, at most 10% of the homes in the city are not up to the current electric codes the probability that the electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, more than 10% of the homes are not up to the current electric codes 55. A consumer protection company is testing a towel rack to see how much force it can hold. The null hypothesis, H0, is that the rack can hold at least 100 pounds of force. The alternative hypothesis, Ha, is that the rack can hold less than 100pounds of force. What is a Type I error in this scenario? Select the correct answer below: The researchers conclude that the rack holds at least 100 pounds of force, but the rack actually holds less than 100 pounds. The researchers conclude that the rack holds less than 100 pounds of force, but the rack actually holds more than 100 pounds. The researchers conclude that the rack holds less than 100 pounds of force, and the rack actually holds less than 100 pounds. The researchers conclude that the rack holds more than 100 pounds of force, and the rack actually holds more than 100 pounds. 56. Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 years. What is the Type II error in this scenario? You think the mean age of the horses on a ranch is 6 years when, in fact, it is. You think the mean age of the horses on a ranch is 6 years when, in fact, it is not. You think the mean age of the horses is not 6 years when, in fact, it is. You think the mean age of the horses is not 6 years when, in fact, it is not. 57. Determine the Type I error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250 pounds and less. MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 61. Which of the following results in a null hypothesis p≤0.69 and alternative hypothesis p>0.69? MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Select the correct answer below: A mechanic wants to show that the percentage of car owners that follow a normal maintenance schedule is not 69%, contrary to a study that found that the percentage was 69%. A mechanic wants to show that more than 69% of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was at most 69%. A mechanic wants to show that at most 69% of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was more than 69%. A mechanic wants to show that less than 69% of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was at least 69%. 62. A city wants to show that the mean number of public transportation users per day is more than 5,575. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. Select the correct answer below: H0: μ≥5,575; Ha: μ<5,575 H0: μ<5,575; Ha: μ≥5,575 H0: μ≤5,575; Ha: μ>5,575 H0: μ>5,575; Ha: μ≤5,575 63. In 2015, the CDC analyzed whether American adults were eating enough fruits and vegetables. Let the mean cups of vegetables adults eat in a day be μ. If the analysts wanted to know if adults were eating, on average, at least the recommended 2 cups of vegetables a day, what are the null and alternative hypothesis? Select the correct answer below: H0: μ<2; Ha: μ>2 H0: μ<2; Ha: μ≥2 H0: μ>2; Ha: μ≥2 H0: μ≥2; Ha: μ<2 H0: μ=2; Ha: μ≠2 H0: μ=2; Ha: μ≥2 MATH 225N Week 7 Hypothesis Testing Question and Answers lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 67. Is the test below left-, right-, or two-tailed? H0:p=0.39, Ha:p≠0.39 Select the correct answer below: MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ The hypothesis test is two-tailed. The hypothesis test is left-tailed. The hypothesis test is right-tailed. 68. Which type of test is used in the following scenario: A manufacturer claims that the mean lifetime of a new cutting blade is 2 years. Fourteen blades are randomly selected and their lifetime is measured. Assume the population follows a normal distributions with known standard deviation. The test is right-tailed because the alternative hypothesis is Ha:μ>2. The test is left-tailed because the alternative hypothesis is Ha:μ<2. The test is right-tailed because the alternative hypothesis is Ha:μ<2. The test is left-tailed because the alternative hypothesis is Ha:μ>2. The test is two-tailed because the alternative hypothesis is Ha:μ≠2. 69. Which graph below corresponds to the following hypothesis test? H0:p≤8.1, Ha:p>8.1 70. Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80% of the time. Which of the following gives β, the probability of a Type II error? Select the correct answer below: MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and AnswersLatest Update 2023 Rated A+ the probability that doctors think the surgical procedure is successful less than 80% of the time when, in fact, it really is successful less than 80% of the time the probability that doctors think the surgical procedure is successful less than 80% of the time when, in fact, it is successful at least 80% of the time the probability that doctors think the surgical procedure is successful at least 80% of the time when, in fact, it is not the probability that doctors think the surgical procedure is successful at least 80% of the time when, in fact, it is MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 74. Which of the following results in a null hypothesis μ≥31 and alternative hypothesis μ<31? Select the correct answer below: MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ A hospital claims that the mean wait time for emergency room patients is at most 31 minutes. A group of researchers think this is inaccurate and wants to show that the mean wait time is more than 31 minutes. A hospital claims that the mean wait time for emergency room patients is more than 31 minutes. A group of researchers think this is inaccurate and wants to show that the mean wait time is less than 31 minutes. A hospital claims that the mean wait time for emergency room patients is at least 31 minutes. A group of researchers think this is inaccurate and wants to show that the mean wait time is less than 31 minutes. A hospital claims that the mean wait time for emergency room patients is 31 minutes. A group of researchers think this is inaccurate and wants to show that the mean wait time is not 31 minutes. 75. Which of the following results in a null hypothesis μ≤7 and alternative hypothesis μ>7? Select the correct answer below: A study wants to show that the mean number of hours of sleep the average person gets each day is at least 7. A study wants to show that the mean number of hours of sleep the average person gets each day is 7. A study wants to show that the mean number of hours of sleep the average person gets each day is more than 7. A study wants to show that the mean number of hours of sleep the average person gets each day is at most 7. 76. A commonly cited study says that 49% of students study less than 5 hours per week. A researcher does not think this is accurate and wants to show that the percentage of students that study less than 5 hours per week is not equal to 49%. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. Select the correct answer below: H0: p≠0.49; Ha: p=0.49 H0: p≥0.49; Ha: p<0.49 H0: p=0.49; Ha: p≠0.49 H0: p≤0.49; Ha: p>0.49 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ lOMoARcPSD|3013804 MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update 2023 Rated A+ 77. Horace, a golfer, claims that his drive distance is less than 225 meters, on average. Several of his friends do not believe him, so he decides to do a hypothesis test, at a 10% significance level, to persuade them. He hits 23 drives. The mean distance of the sample drives is 210 meters. Horace knows from experience that the standard deviation for his drive distance is 14meters. • H0: μ≥225; Ha: μ<225 • α=0.1 (significance level) MATH 225N Week 7 Hypothesis Testing Question and Answers Latest Update