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A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.1 ounces of coffee per cup. BIG has good reason to believe that the mean amount of coffee dispensed by the machine, u, is less than 7.1 ounces, and plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 6.8 ounces and that the standard deviation is 0.3 ounces. Based on this information, complete the parts below. (a) What are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? H : 0 H : 1 020 0=0 0*0 (b) Suppose that BIG decides not to reject the null hypothesis. What sort of error might it be making? (Choose one) X 5 ? (c) Fill in the blanks to describe the Type II error that could occur if the true mean amount of coffee dispensed by the machine is 6.6 ounces. A Type II error would be (Choose one) the hypothesis that u is (Choose one) (Choose one) V when, in fact, u is (Choose one)Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, M, spent by customers at the supermarkets has been reported to be 38 minutes, but executives have good reason to believe that u is different from 38 minutes. The executives hire a statistical consultant and ask her to perform a statistical test. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 45 minutes and the standard deviation of the times to be 16 minutes. Based on this information, complete the parts below. (a) What are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? X Ho : 0 020 0=0 0#0 (b) Suppose that the consultant decides to reject the null hypothesis. What sort of error might she be making? (Choose one) V X (c) Fill in the blanks to describe the Type II error that could occur if the true mean shopping time spent by customers at the supermarkets is 48 minutes. A Type II error would be (Choose one) the hypothesis that u is (Choose one) (Choose one) V when, in fact, u is (Choose one)Managers at an automobile manufacturing plant would like to examine the mean completion time, J, of an assembly line operation. The past data indicate that the mean completion time is 43 minutes, but the managers have good reason to believe that this value has increased. The managers plan to perform a statistical test. After choosing a random sample of assembly line completion times, the managers compute the sample mean completion time to be 45 minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of 5 minutes. Based on this information, complete the parts below. (a) What are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? X Ho : 0 020 0=0 0*0 (b) Suppose that the managers decide not to reject the null hypothesis. What sort of error might they be making? (Choose one) X 5 ? (c) Fill in the blanks to describe the Type I error that could occur if the true mean completion time for the assembly line operation is 43 minutes. A Type I error would be (Choose one) the hypothesis that u is (Choose one) (Choose one) when, in fact, u is (Choose one)The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0016. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0016. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis , and the alternative hypothesis /, that we would use for this test. He : X p H1: 0 O S 00 020 0=0 0#0 X ?The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a standard deviation of 0.06. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.06. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis , and the alternative hypothesis H, that we would use for this test. He : I X P H : I S S0 0>0 020 0=0 0*0 X ?The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis Ho and the alternative hypothesis , that we would use for this test. Ho : X p H : I S 00 020 0=0 0*0 X ?An old medical textbook states that the mean sodium level for healthy adults is 138 mEq per liter of blood. A medical researcher believes that, because of modern dietary habits, the mean sodium level for healthy adults, u, now differs from that given in the textbook. A random sample of 60 healthy adults is evaluated. The mean sodium level for the sample is 142 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 13 mEq. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level differs from that given in the textbook? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H. H O P Ho : I X S P H : 1 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 0 X ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the population mean adult sodium level differs from that given in the textbook? Yes ONoThe records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a standard deviation of 0.06. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.06. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis Ho and the alternative hypothesis H, that we would use for this test. X p H: I p S OSO >0 020 0=0 0*0 X ?Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 13.2 minutes. The standard deviation of completion times was 1.8 minutes. An analyst at the company suspects that, under new management, the mean completion time, u, is now less than 13.2 minutes. To test this claim, a random sample of 28 completion times under new management was taken by the analyst. The sample had a mean of 12.9 minutes. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean completion time under new management is less than 13.2 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. O P Ho : 0 X S P H, : 0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 0 X 5 (d) Find the p-value. (Round to three or more decimal places.) ? 0 (e) Can we support the claim that the population mean completion time under new management is less than 13.2 minutes? Yes ONoAccording to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 51 months. A researcher for a consumer advocate group tests this by selecting 23 bulbs at random. For the bulbs in the sample, the mean lifetime is $3 months. It is known that the population standard deviation of the lifetimes is 9 months. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the population mean lifetime, H, of light bulbs made by this manufacturer differs from 51 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H. O P H : 0 X S P H :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 0 X 5 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the population mean lifetime of light bulbs made by this manufacturer differs from 51 months? Yes ONo