Exam 13: Confidence Intervals and Hypothesis Tests for Means

Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. -A Type II error in this context would be

Consider the following to answer the question(s) below: The Dispenser Right Company makes a soft drink dispensing machine used in many fast food restaurants. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by a particular machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed: -The 99% confidence interval is

Consider the following to answer the question(s) below: A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours. -What is the associated P-value?

Suppose 40 professional employees are randomly selected. This sample yields a mean of 15.2 hours and a standard deviation of 1.8 hours. Find the 95% confidence interval and interpret.

Consider the following to answer the question(s) below: A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours. -What is the value of the test statistic?

Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. -What is the value of the test statistic?

Suppose 40 professional employees are randomly selected. This sample yields a mean of 15.2 hours and a standard deviation of 1.8 hours. The 95% confidence interval is

Consider the following to answer the question(s) below: A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours. -In this context, describe the Type II error possible. How might such an error impact the software development firm?

Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. -In this context, describe the Type II error possible. How might such an error impact ABI Insurance?

Consider the following to answer the question(s) below: A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours. -State your conclusion using α = 0.05.

Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. -Write the null and alternative hypotheses.

Consider the following to answer the question(s) below: A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours. -The correct value of the test statistic is

Consider the following to answer the question(s) below: The cost of a university education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average number of hours students work per week exceeds 20. A random sample of 20 students was selected and the following values were observed: -The correct null and alternative hypotheses are

Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. -The P-value associated with the test statistic is

Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. -In this context, describe the Type I error possible. How might such an error impact ABI Insurance?

Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. -For more accurate cost determination, ABI Insurance wants to estimate the average life expectancy to within one year with 95% confidence. How many randomly selected recently paid policies would they need to sample?