MATHS 221 Week 6 Homework

MATHS 221 Week 6 Homework 1. A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 36 months. Write the null and alternative hypotheses and note which is the claim. Ho: μ ...

MATHS 221 Week 6 Homework 1. A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 36 months. Write the null and alternative hypotheses and note which is the claim. Ho: μ > 36, Ha: μ ≤ 36 (claim) Ho: μ = 36 (claim), Ha: μ ≥ 36 Ho: μ ≤ 36, Ha: μ > 36 (claim) Ho: μ ≤ 36 (claim), Ha: μ > 36 2. 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 (claim), Ha: μ > 9.2 Ho: μ ≤ 9.2 (claim), Ha: μ > 9.2 Ho: μ > 9.2, Ha: μ ≤ 9.2 (claim) Ho: μ ≥ 9.2, Ha: μ ≤ 9.2 (claim) 3. An amusement park claims that the average daily attendance is at least 10,000. Write the null and alternative hypotheses and note which is the claim. Ho: μ ≤ 10000, Ha: μ > 10000 (claim) Ho: μ ≥ 10000 (claim), Ha: μ < 10000 Ho: μ > 10000 (claim), Ha: μ = 10000 Ho: μ = 10000, Ha: μ ≤ 10000 (claim) 4. A transportation organization claims that the mean travel time between two destinations is about 17 minutes. Write the null and alternative hypotheses and note which is the claim. Ho: μ = 17 (claim), Ha: μ ≠ 17 Ho: μ > 17, Ha: μ ≤ 17 (claim) Ho: μ ≠ 17, Ha: μ = 17 (claim) >Ho: μ = 17 (claim), Ha: μ ≤ 17 5. Type I and type II errors occur because of what issue within the hypothesis testing process?The population is not a representative subset of the sample The sample taken is not representative of the population The math calculations were done incorrectly The sample mean is different than the population mean 6. 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 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 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 7. 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 not sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage There is sufficient evidence to support the claim that less 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 There is sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage 8. A sprinkler manufacturer claims that the average activating temperatures is at most 131 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 p-value. z-test statistic = 3.43, p-value = 0.0006 z-test statistic = -3.43, p-value = 0.0003 z-test statistic = 3.43, p-value = 0.0003 z-test statistic = -3.43, p-value = 0.00069. A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 6.8 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 p-value. z-test statistic = -1.998, p-value = 0.046 z-test statistic = 1.998, p-value = 0.023 z-test statistic = -1.998, p-value = 0.023 z-test statistic = 1.998, p-value = 0.046 10. 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 12- ounce bottles of caffeinated soft drinks that has a mean caffeine content of 32.8 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic? >Claim is null, reject the null and reject claim as test statistic (-2.77) is in the rejection region defined by the critical value (-1.96) Claim is alternative, fail to reject the null and support claim as test statistic (-2.77) is not in the rejection region defined by the critical value (-1.64) Claim is alternative, reject the null and support claim as test statistic (-2.77) is in the rejection region defined by the critical value (-1.64) Claim is null, fail to reject the null and reject claim as test statistic (-2.77) is not in the rejection region defined by the critical value (-1.96) 11. 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, 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, 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)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) 12. 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 8.28 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 p-value? Claim is alternative, reject the null and cannot support claim as the p-value (0.085) is greater than alpha (0.02) Claim is null, reject the null and cannot support claim as the p-value (0.170) is less than alpha (0.02) Claim is alternative, fail to reject the null and support claim as the p-value (0.085) is less than alpha (0.02) Claim is null, fail to reject the null and support claim as the p-value (0.170) is greater than alpha (0.02) 13. 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 26.75 inches. The population standard deviation is assumed to be 0.15 inches. At α=0.05, should the business reject the supplier’s claim? No, since p>α, we reject the null and the null is the claim Yes, since p<α, we reject the null and the null is the claim No, since p>α, we fail to reject the null and the null is the claim Yes, since p>α, we fail to reject the null and the null is the claim 14. 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 p<α, we reject the null. The claim is the alternative, so the claim is supported No, since p>α, we fail to reject the null. The claim is the alternative, so the claim is not supported Yes, since p>α, we fail to reject the null. The claim is the null, so the claim is supported No, since p<α, we reject the null. The claim is the alternative, so the claim is not supported15. 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 0.14 minutes. Can the claim be supported at α=0.08? No, 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 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 Yes, 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 supported 16. In a hypothesis test, the claim is μ≤40 while the sample of 27 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 known t test statistic would be used as the standard deviation is less than 10 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 mean is greater than 30 17. 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 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 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 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 supported18. 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 p-value of 0.30 is greater than 0.10, fail to reject the null. Claim is null, so is supported No, since p-value of 0.30 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported No, since p-value of 0.30 is greater than 0.10, reject the null. Claim is null, so is not supported Yes, since p-value of 0.30 is less than 0.54, reject the null. Claim is alternative, so is supported 19. A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of five cars form this company have an average gas mileage of 25.2 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 -1.79 is close to the critical value of -2.60, the null is not rejected. The claim is the null, so is supported No, since the test statistic of -1.79 is in the rejection region defined by the critical value of -1.97, the null is rejected. The claim is the null, so is not supported Yes, since the test statistic of -1.79 is not in the rejection region defined by the the critical value of -2.60, the null is rejected. The claim is the null, so is supported Yes, since the test statistic of -1.79 is not in the rejection region defined by the critical value of -1.97, the null is not rejected. The claim is the null, so is supported 20. A researcher wants to determine if zinc levels are different between the top of a glass of water and the bottom of a glass of water. Many samples of water are taken. From half, the zinc level at the top is measured and from half, the zinc level at the bottom is measured. Would this be a valid matched pair test? No, as the measurements of top and bottom should be from the same glass No, as the zinc levels cannot be accurately measured Yes, as long as they are all from the same faucet Yes, as long as there are an equal number of glasses in each group