MATH 225N MATH Week 7 Hypothesis Testing Questions and Answers, Exams of Nursing

Download MATH 225N MATH Week 7 Hypothesis Testing Questions and Answers and more Exams Nursing in PDF only on Docsity! 1 Week 7 Hypothesis Testing Q & A 1. 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 more often than not. 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 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 (≠) ± 0.64000 0 0.50000 0 0.07071 1 1.97989 9 0.02385 2 0.04770 4 1.644854 -1.644854 1.959964 2 (decimal ) (decimal ) Answer: Reject the null hypothesis. There is sufficient evidence to prove that Steve will like a random selected song more often than not. 2. 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. 0.05 0.5000 50 32 5 One-Sided p-value Two-Sided p-value Right-Tailed (>) Left-Tailed (<) Two-Tailed (≠) ± Answer: 0.063 4. A researcher claims that the incidence of a certain type of cancer is < 5%. To test this claim, a random sample of 4000 people are checked and 170 are found to have the cancer. The following is the set up for the hypothesis: Ho = 0.05 Ha = < 0.05 In the example the p-value was determined to be 0.015. Come to a conclusion and interpret the results of this hypothesis test for a proportion (use a significance level of 5%) Answer: The decision is to reject the null hypothesis. The conclusion is that there is enough evidence to support the claim. 5. A researcher is investigating a government claim that the unemployment rate is < 5%. TO test this claim, a random sample of 1500 people is taken and it is determined that 61 people were unemployed. Ho: p = 0.05 Ha: p < 0.05 Find the p-value for this hypothesis test for a proportion & round to 3 decimal places. Hypothesis Test for p population proportion Level of Significance Proportion under H0 n 0.05 0.0500 1500 61 1.530613 0.063008 0.126016 1.644854 -1.644854 1.959964 6 Number of Successes Sample Proportion StDev SE Test Statistic (z) 0.04066 7 0.21794 5 0.00562 7 - 1.65857 7 One-Sided p-value Two-Sided p-value Answer: 0.048 6. 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 Level of Significance Proportion under H0 n Number of Successes Sample Proportion StDev SE 7 0.04845 7 0.09691 4 0.05 0.6500 750 513 0.68400 0 0.47697 0 0.01741 6 1.95217 5 0.02558 8 10 10. A hospital administrator claims that the proportion of knee surgeries that are successful are 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 patients had a successful knee surgery operation. Ho: p = 0.87 Ha: p ≠ 0.87 (two sided tail) Find the test statistics for this hypothesis test for a proportion & round to 2 decimal places. Answer: -2.87 (this would be rejected) Level of 0.05 11 Significance Proportion under H0 n Number of Successes Sample Proportion StDev SE Test Statistic (z) One-Sided p-value Two-Sided p-value 11. Jose, a competitor in cup stacking, has a sample stacking time mean of 7.5 seconds from 13 trials. Jose still claims that his average stacking time is 8.5 seconds, and the low average can be contributed to chance. At the 2% significant level, does the data provide sufficient evidence to conclude that Jose’s mean stacking time is less than 8.5 seconds? Given the sample data below, select or reject the hypothesis. (If p=value is < alpha value, we would automatically reject the hypothesis) Ho: μ = 8.5 Ha: μ = <8.5 α = 0.02 (significance level) Zo = -2.18 P = 0.0146 Answer: Reject the null hypothesis because the p value 0.0146 is less than the significance level 0.02 12. 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 0.8700 450 371 0.824444 0.336303 0.015853 -2.873534 0.002052 0.004104 12 13. 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 14. 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) 15 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: 0.131 18. 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: 0.05 0.4000 400 149 0.37250 0 0.48989 8 0.02449 5 - 1.12268 3 0.13135 7 0.26271 4 16 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. 17 (So, if p≤α, reject H0; otherwise fail to reject H0) 19. 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. 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. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim. 20. 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 20 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. 23. A researcher claims that the proportion of people who are right-handed is 70%. To test this claim, a random sample of 600 people is taken and its determined that 397 people are right handed. The following is the setup for this hypothesis test: H0:p = 0.70 Ha:p ≠ 0.70 21 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. Answer: 0.040 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 24. 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) 0.05 0.7000 600 397 0.66166 7 0.45825 8 0.01870 8 - 2.04900 3 0.02018 2 0.04036 4 22 • 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. 25 Thus the conclusion is that there is enough evidence to reject the claim. 27. Shawn, a competitor in cup stacking, has a sample stacking time mean of 9.2 seconds from 13 trials. Shawn still claims that her average stacking time is 8.5 seconds, and the high average can be attributed to chance. At the 4% significance level, does the data provide sufficient evidence to conclude that Shawn's mean stacking time is greater than 8.5 seconds? Given the sample data below, accept or reject the hypothesis. • H0:μ=8.5 seconds; Ha:μ>8.5 seconds • α=0.04 (significance level) • z0=0.61 • p=0.2709 Select the correct answer below: Do not reject the null hypothesis because 0.61>0.04. Reject the null hypothesis because the value of z is positive. Reject the null hypothesis because 0.61>0.04. Reject the null hypothesis because the p-value 0.2709 is greater than the significance level α=0.04. Do not reject the null hypothesis because the p-value 0.2709 is greater than the significance level α=0.04. 28. Ruby, a bowler, has a sample game score mean of 125.8 from 25 games. Ruby still claims that her average game score is 140, and the low average can be attributed to chance. At the 5% significance level, does the data provide sufficient evidence to conclude that Ruby's mean game score is less than 140? Given the sample data below, accept or reject the hypothesis. • H0:μ=140; Ha:μ<140 • α=0.05 (significance level) • z0=−0.52 • p=0.3015 26 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. 27 29. 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. 30. 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. 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 30 Which answer choice shows the correct null and alternative hypotheses for this test? H0:p=0.26; Ha:p>0.26, which is a right-tailed test. (a) H0:p=0.2; Ha:p<0.2, which is a left-tailed test. (b) H0:p=0.26; Ha:p≠0.26, which is a two-tailed test. (c) H0:p=0.2; Ha:p≠0.2, which is a two-tailed test. 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. 31 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 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. 0.05 0.2000 50 13 0.260000 0.400000 0.056569 1.060660 0.144572 0.289144 32 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) 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. 35 40. Colton makes the claim to his classmates that less than 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 are boys. What are the null and alternative hypotheses for this hypothesis test? Select the correct answer below: H0:p≠0.5 Ha:p=0.5 H0:p=0.5 Ha:p≠0.5 H0:p=0.5 Ha:p>0.5 H0:p=0.5 Ha:p<0.5 41. Kylie works for a large nursery and is investigating whether to use a new brand of seeds. The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. She will change over to this new brand unless the actual germination rate is less than what is advertised. Kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. She finds that 70 of those seeds germinated. What are the null and alternative hypotheses for this hypothesis test? Select the correct answer below: H0:p=0.93 Ha:p>0.93 H0:p=0.93 Ha:p<0.93 H0:p≠0.93 Ha:p=0.93 H0:p=0.93 Ha:p≠0.93 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 36 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? 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 37 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 Level of Significance Proportion under H0 n Number of Successes 0.05 0.1100 1000 126 40 Test Statistic (z- score) One-Sided p-value Two-Sided p-value 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. 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. 41 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 42 Level of Significance Mean under H0 n Sample Mean StDev SE Test Statistic (z- score) One-Sided p-value Two-Sided p-value 0.01 43 19 35 6 1.376494 -5.811865 0.000000 0.000000 45 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: 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. 46 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: 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 47 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. 50 H0: p≤0.44; Ha: p>0.44 H0: p<0.44; Ha: p≥0.44 H0: p>0.44; Ha: p≤0.44 H0: p≥0.44; Ha: p<0.44 61. Which of the following results in a null hypothesis p≤0.69 and alternative hypothesis p>0.69? Select the correct answer below: 51 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 52 64. Which of the following results in a null hypothesis p≤0.47 and alternative hypothesis p>0.47? Select the correct answer below: An online article claims that less than 47% of internet users participate in social media. A group of researchers think this is incorrect, and they want to show that at least 47% of internet users participate in social media. 55 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: 56 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 57 71. Determine the Type I error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Select the correct answer below: The researchers think that greater than or less than 65% of college students will graduate with debt when, in fact, 65% will graduate with debt. The researchers think that 65% of college students will graduate with debt when, in fact, more or less than 65%of college students will graduate with debt. The researchers think that 65% of college students will graduate with debt when, in fact, 65% of college students really will graduate with debt. The researchers think that greater than or less than 65% of college students will graduate with debt when, in fact, greater than or less than 65% of college students will graduate with debt. 72. Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is β, the probability of a Type II error in this scenario? the probability that the sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores the probability that the sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores the probability that the sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores the probability that the sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores 73. Determine the Type II error if the null hypothesis, H0, is: the mean price of a loaf of bread is $1.67. Select the correct answer below: 60 H0: p≥0.49; Ha: p<0.49 H0: p=0.49; Ha: p≠0.49 H0: p≤0.49; Ha: p>0.49 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. 61 • H0: μ≥225; Ha: μ<225 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Provide your answer below: -5.14 William, a chef, claims that his meatball weight is not equal to 3 ounces, on average. Several of his customers do not believe him, so he decides to do a hypothesis test, at a 1% significance level, to persuade them. He cooks 19 meatballs. The mean weight of the sample meatballs is 2.9 ounces. William knows from experience that the standard deviation for his meatball weight is 0.5 ounces. • H0: μ=3; Ha: μ≠3 • α=0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Provide your answer below: -.87