MATH 221 Week 6 Quiz (GRADED A) Questions and Answer Elaborations | DeVry University

. MATH 221 Week 6 Quiz A consumer analyst reports that the mean life of a certain type of alkaline battery is more than 63 months. Write the null and alternative hypotheses and note which is the cl aim. Ho: μ ≤ 63, Ha: μ 63 (claim) Ho: μ 63 (claim), Ha: μ ≤ 63 Ho: μ = 63 (claim), Ha: μ ≥ 63 Ho: μ ≤ 63, Ha: μ 63 (claim) A business claims that the mean time that customers wait for service is at most 9.2 minutes. Write the null and alternative hypotheses and note which is the claim. Ho: μ 9.2, Ha: μ ≤ 9.2 (claim) Ho: μ ≥ 9.2, Ha: μ ≤ 9.2 (claim) Ho: μ ≤ 9.2 (claim), Ha: μ 9.2 Ho: μ 9.2 (claim), Ha: μ 9.2 An amusement park claims that the average daily attendance is at least 15,000. Write the null and alternative hypotheses and note which is the claim. Ho: μ ≥ 15000 (claim), Ha: μ 15000 Ho: μ 15000 (claim), Ha: μ = 15000 Ho: μ = 15000, Ha: μ ≤ 15000 (claim) Ho: μ ≤ 15000, Ha: μ 15000 (claim) A transportation organization claims that the mean travel time between two destinations is about 12 minutes. Write the null and alternative hypotheses and note which is the claim. Ho: μ = 12 (claim), Ha: μ ≠ 12 Ho: μ = 12 (claim), Ha: μ ≤ 12 Ho: μ 12, Ha: μ ≤ 12 (claim) Ho: μ ≠ 12, Ha: μ = 12 (claim) Question 5 2 / 2 pts Type I and type II errors occur because of what issue within the hypothesis testing process? The math calculations were done incorrectly The sample mean is different than the population mean The population is not a representative subset of the sample The sample taken is not representative of the population A scientist claims that the mean gestation period for a fox is 51.5 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? There is enough evidence to support the scientist’s claim that the gestation period is 51.5 weeks There is not enough evidence to support the scientist’s claim that the gestation period is more than 51.5 weeks There is not enough evidence to support the scientist’s claim that the gestation period is 51.5 weeks The evidence indicates that the gestation period is less than 51.5 weeks Question 7 2 / 2 pts A marketing organization claims that more than 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? There is sufficient evidence to support the claim that less than 10% of the employees are paid minimum wage There is sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage There is not sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage There is not sufficient evidence to support the claim that 10% of the employees are paid minimum wage A sprinkler manufacturer claims that the average activating temperatures is at least 135 degrees. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. Assume the population standard deviation is 3.3 degrees. Find the standardized test statistic and the corresponding p­value. z­test statistic = ­3.43, p­value = 0.0003 z­test statistic = 3.43, p­value = 0.0003 z­test statistic = ­3.43, p­value = 0.0006 z­test statistic = 3.43, p­value = 0.0006 A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 7.0 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.6 seconds. Assume the population standard deviation is 2.3 seconds. Find the standardized test statistic and the corresponding p­value. z­test statistic = ­1.499, p­value = 0.134 z­test statistic = 1.499, p­value = 0.134 z­test statistic = ­1.499, p­value = 0.067 z­test statistic = 1.499, p­value = 0.067 A consumer research organization states that the mean caffeine content per 12­ ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12­ounce bottles of caffeinated soft drinks that has a mean caffeine content of 35.2 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, do you support or reject the organization’s claim using the test statistic? Claim is alternative, fail to reject the null and support claim as test statistic (­1.44) is not in the rejection region defined by the critical value (­1.64) Claim is null, reject the null and reject claim as test statistic (­1.44) is in the rejection region defined by the critical value (­1.96) Claim is alternative, reject the null and reject claim as test statistic (­ 1.44) is in the rejection region defined by the critical value (­1.64) Claim is null, fail to reject the null and support claim as test statistic (­ 1.44) is not in the rejection region defined by the critical value (­1.96) A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.6 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you support the organization’s claim using the test statistic? Claim is alternative, reject the null and support claim as test statistic (­ 1.78) is not in the rejection region defined by the critical value (­2.05) Claim is null, fail to reject the null and cannot support claim as test statistic (­1.78) is not in the rejection region defined by the critical value (­2.05) Claim is null, reject the null and cannot support claim as test statistic (­ 1.78) is not in the rejection region defined by the critical value (­2.05) Correct Answer Claim is alternative, fail to reject the null and cannot support claim as test statistic (­1.78) is not in the rejection region defined by the critical value (­2.05) A pharmaceutical company claims that the average cold lasts an average of 8.4 days. They are using this as a basis to test new medicines designed to shorten the length of colds. A random sample of 106 people with colds, finds that on average their colds last 8.6 days. The population is normally distributed with a population standard deviation of 0.9 days. At α=0.02, what type of test is this and can you support the company’s claim using the p­value? Claim is alternative, reject the null and cannot support claim as the p­value (0.011) is greater than alpha (0.02) Claim is null, fail to reject the null and support claim as the p­value (0.022) is greater than alpha (0.02) Claim is alternative, fail to reject the null and cannot support claim as the p­value (0.011) is less than alpha (0.02) Claim is null, reject the null and support claim as the p­value (0.022) is less than alpha (0.02) A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim? Correct Answer Yes, since pα, we reject the null and the null is the claim No, since pα, we reject the null and the null is the claim Yes, since pα, we fail to reject the null and the null is the claim No, since pα, we fail to reject the null and the null is the claim Question 14 2 / 2 pts The company’s cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 47.6 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10? Yes, since pα, we fail to reject the null. The claim is the null, so the claim is supported Yes, since pα, we reject the null. The claim is the alternative, so the claim is supported No, since pα, we fail to reject the null. The claim is the alternative, so the claim is not supported No, since pα, we reject the null. The claim is the alternative, so the claim is not supported A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.26 minutes. The population standard deviation is assumed to be 0.29 minutes. Can the claim be supported at α=0.08? Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported No, since test statistic is not in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is not supported No, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported In a hypothesis test, the claim is μ≤28 while the sample of 29 has a mean of 41 and a sample standard deviation of 5.9 from a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why? z test statistic would be used as the population standard deviation is unknown Correct Answer t test statistic would be used as the data are normally distributed with an unknown population standard deviation z test statistic would be used as the population standard deviation is known t test statistic would be used as the data set is small and the population standard deviation is known A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of nine professors finds that the mean time in their offices is 6.1 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05? Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported Correct Answer No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3547 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set? Yes, since p­value of 0.30 is less than 0.54, reject the null. Claim is alternative, so is supported Correct Answer No, since p­value of 0.30 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported No, since p­value of 0.30 is greater than 0.10, reject the null. Claim is null, so is not supported Yes, since p­value of 0.30 is greater than 0.10, fail to reject the null. Claim is null, so is supported A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set? No, since the test statistic of ­1.41 is close to the critical value of ­1.24, the null is not rejected. The claim is the null, so is supported Yes, since the test statistic of ­1.41 is not in the rejection region defined by the critical value of ­1.55, the null is rejected. The claim is the null, so is supported Yes, since the test statistic of ­1.41 is not in the rejection region defined by the critical value of ­1.77, the null is not rejected. The claim is the null, so is supported No, since the test statistic of ­1.41 is in the rejection region defined by the the critical value of ­1.77, the null is rejected. The claim is the null, so is not supported A researcher wants to determine if daily walks together strengthen a marriage. One group of wives and one group of husbands are selected and take walks each day. After 2 weeks, all are asked if they felt their marriage was stronger based on the walks and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups? That the both groups were positive on marriage before the walks That the husbands and wives selected were married to each other That all husbands and wives in the test had been married about the same amount of time That the wives group was positive on marriage before the walks Quiz Score: 30 out of 40 Current Score: 30 out of 40 Kept Score: 30 out of 40 Show Less