WEEK 7 HYPOTHESIS TESTING QUESTIONS AND ANSWERS., Exams of Nursing

Download WEEK 7 HYPOTHESIS TESTING QUESTIONS AND ANSWERS. and more Exams Nursing in PDF only on Docsity! WEEK 7 HYPOTHESIS TESTING QUESTIONS AND ANSWERS 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 equationhere . 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 0.05 (decimal ) Proportion under H0 0.5000 (decimal ) n 50 Number of Successes 32 Sample Proportion 0.64000 0 StDev 0.50000 0 SE 0.07071 1 Test Statistic (z) 1.97989 9 One-Sided p-value 0.02385 2 Two-Sided p-value 0.04770 4 Right-Tailed (>) 1.644854 Left-Tailed (<) -1.644854 Two-Tailed (≠) ± 1.959964 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. 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 so leave it 0.05) Hypothesis Test for p population proportion Level of Significance 0.05 Proportion under H0 0.5000 n 200 Number of Successes 108 Sample Proportion 0.540000 StDev 0.500000 SE 0.035355 Test Statistic (z) 1.131371 One-Sided p-value 0.129238 Two-Sided p-value 0.258476 Right-Tailed (>) 1.644854 7 Two-Sided p-value 0.09691 4 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 0.05 Proportion under H0 0.6500 n 750 Number of Successes 513 Sample Proportion 0.68400 0 StDev 0.47697 0 SE 0.01741 6 Test Statistic (z) 1.95217 5 One-Sided p-value 0.02558 8 Two-Sided p-value 0.05117 6 Answer: 0.026 7. 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 8. 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 9. 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 0.05 Proportion under H0 0.4000 n 400 Number of Successes 190 Sample Proportion 0.475000 StDev 0.489898 SE 0.024495 Test Statistic (z) 3.061862 One-Sided p-value 0.001107 Two-Sided p-value 0.002214 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 Significance 0.05 Proportion under H0 0.8700 n 450 Number of Successes 371 Sample Proportion 0.824444 StDev 0.336303 SE 0.015853 Test Statistic (z) -2.873534 One-Sided p-value 0.002052 Two-Sided p-value 0.004104 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 Level of Significance 0.05 Proportion under H0 0.4000 n 400 Number of Successes 149 Sample Proportion 0.37250 0 StDev 0.48989 8 SE 0.02449 5 Test Statistic (z) - 1.12268 3 One-Sided p-value 0.13135 7 Two-Sided p-value 0.26271 4 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: 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) 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 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 21.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. 22.A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700 people is taken in the city and 150 people indicate they are smokers. The following is the setup for this hypothesis test: 25.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. 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. 26.Elizabeth claims that her average typing speed is at least 87 words per minute From recent typing trials, it is observed that Elizabeth has a sample typing speed mean of 98.9 words per minute (based on 18 trials). Given the sample data below, determine whether to reject the null hypothesis, or fail to reject the null hypothesis and also come to a conclusion regarding the claim. H0:μ=87 words per minute; Ha:μ<87 words per minute α=0.01 (significance level) z0=1.92 p=0.0274 Select the correct answer below: The decision is to fail to reject the null hypothesis. Thus the conclusion is that there is not enough evidence to reject the claim. The decision is to reject the null hypothesis. Thus the conclusion is that there is not enough evidence to reject the claim. The decision is to fail to reject the null hypothesis. 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 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. 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: (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. 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 0.05 Proportion under H0 0.2000 n 50 Number of Successes 13 Sample Proportion 0.260000 StDev 0.400000 SE 0.056569 Test Statistic (z) 1.060660 One-Sided p-value 0.144572 Two-Sided p-value 0.289144 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. 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.  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 0.05 Proportion under H0 0.2500 n 250 Number of Successes 60 Sample Proportion 0.24000 0 StDev 0.43301 3 SE 0.02738 6 Test Statistic (z) - 0.36514 8 One-Sided p-value 0.35569 1 Two-Sided p-value 0.71138 2 Provide your answer below: -.37 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 Successes Sample Proportion 0.12600 0 StDev 0.31289 0 SE 0.00989 4 Test Statistic (z) 1.61706 9 One-Sided p-value 0.05261 6 Two-Sided p-value 0.10523 2 Provide your answer below: 1.62 45.Rosetta, a pitcher, claims that her pitch speed is more than 57 miles per hour, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She throws 10 pitches. The mean speed of the sample pitches is 64 miles per hour. Rosetta knows from experience that the standard deviation for her pitch speed is 4 miles per hour. H0: μ≤57; Ha: μ>57 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: 5.53 Hypothesis Test for µ Population stdev known Level of Significance 0.01 Mean under H0 57 n 10 Sample Mean 64 StDev 4 SE 1.26491 1 Test Statistic (z- score) 5.53398 6 One-Sided p-value 0.00000 0 Two-Sided p-value 0.00000 0 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. 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 0.01 Mean under H0 43 n 19 Sample Mean 35 StDev 6 SE 1.376494 Test Statistic (z- score) -5.811865 One-Sided p-value 0.000000 Two-Sided p-value 0.000000 Provide your answer below: -5.81 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. 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 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. Select the correct answer below: You think the ladder can withstand weight of 250 pounds and less when, in fact, it cannot. You think the ladder cannot withstand weight of   250   pounds and less when, in fact, it really can. You think the ladder can withstand weight of 250 pounds and less when, in fact, it can. You think the ladder cannot withstand weight of 250 pounds and less when, in fact, it cannot. 58. Which of the following answers give valid null and alternative hypotheses for a hypothesis test? Select all correct answers. H0: μ>15; Ha: μ≤15 H0: μ≥15; Ha: μ<15 H0: μ=15; Ha: μ≠15 H0: μ≠15; Ha: μ=15 59.A mattress store advertises that their beds last at least 5 years, on average. A consumer group thinks that they do not last that long and wants to set up a hypothesis test. If μ denotes the average time, in years, that the mattresses last, what are the null and alternative hypotheses in this situation? Select the correct answer below: H0: μ≥5; Ha: μ<5 H0: μ≤5; Ha: μ>5 H0: μ>5; Ha: μ≤5 H0: μ≥5; Ha: μ≤5 H0: μ≤5; Ha: μ≥5 60.A mechanic wants to show that more than 44% of car owners do not follow a normal maintenance schedule. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. Select the correct answer below: than 55 minutes. Identify the group's null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. Select the correct answer below: H0: μ>55; Ha: μ≤55 H0: μ<55; Ha: μ≥55 H0: μ≥55; Ha: μ<55 H0: μ≤55; Ha: μ>55 66. Which graph below corresponds to the following hypothesis test? H0:μ≤16.9, Ha:μ>16.9 67. Is the test below left-, right-, or two-tailed? H0:p=0.39, Ha:p≠0.39 Select the correct answer below: 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: 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 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