Exam 13: Testing Hypotheses

Make conclusions about the hypotheses. -A report on the U.S. economy indicates that 28% of Americans have experienced Difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty. Does this indicate that the Problem is more severe among these cities? The P-value associated with the test statistic For testing this claim is 0.0029. At α = .05,

Write the hypotheses. -A report on the U.S. economy indicates that 28% of Americans have experienced Difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty. Does this indicate that the Problem is more severe among these cities? The correct null and alternative hypotheses For testing this claim are A. $H _ { 0 } : p = 0.28$ and $H _ { A } : p > 0.28$ B. $H _ { 0 } : p = 0.28$ and $H _ { A } : p < 0.28$ C. $H _ { 0 } : p = 0.28$ and $H _ { A } : p \neq 0.28$ D. $H _ { 0 } : p \neq 0.28$ and $H _ { A } : p = 0.28$ E. $H _ { 0 } : p > 0.28$ and $H _ { A } : p = 0.28$

Create a confidence interval for the mean difference. -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.

Find critical values. -Suppose that you are conducting a two tailed test about a proportion at the 0.01 level Of significance. The correct critical value(s) to be used in drawing a conclusion is (are)

Identify the type of test. -A company manufacturing computer chips finds that 8% of all chips manufactured are Defective. In an effort to decrease the percentage of defective chips, management decides To provide additional training to those employees hired within the last year. After Training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis Test is performed to determine if the additional training was effective in lowering the Defect rate. Which of the following statement is true about this hypothesis test?

Create a confidence interval for the mean difference. -Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. One of his recommendations is for the company to conduct seminars for employees in order to disseminate and reinforce the new corporate philosophy. This is done for a six month trial period after which its value in changing employee attitudes will be assessed. a. Write the null and alternative hypotheses. b. In this context, describe the Type I error possible. How might such an error impact the company? c. In this context, describe the Type II error possible. How might such an error impact the company? d. Based on data collected after the trial period, the company constructed a 95% confidence interval for the proportion of all employees open to new ideas and approaches toward their work. The resulting interval is 18% to 22%. What conclusion should the company reach about the seminars? Explain.

Write the hypotheses. -Top management of a large multinational corporation wants to create a culture of Innovativeness and change. A consultant hired to assess the company's organizational Culture finds that only 15% of employees are open to new ideas and approaches toward Their work. Consequently the company conducts a program for employees in order to Reinforce the new corporate philosophy. After the program is completed, employees are Surveyed to see if a greater percentage is now open to innovativeness and change. The Correct alternative hypothesis is A. $p = 0.15$ B. $p > 0.15$ C. $p < 0.15$ D. $\mu > 0.15$ E. $\mu \neq 0.15$

Make conclusions based on confidence intervals. -A company that sells eco-friendly cleaning products is concerned that only 19.5% of People who use such products select their brand. A marketing director suggests that the Company invest in new advertising and labeling to strengthen its green image. The Company decides to do so in a test market so that the effectiveness of the marketing Campaign may be evaluated. Based on data collected in the test market, the company Constructed a 98% confidence interval for the proportion of all consumers who might buy Their brand. The resulting interval is 16% to 28%. What conclusion should the Company reach about the new marketing campaign?

Identify and interpret types of error. -Top management of a large multinational corporation wants to create a culture of Innovativeness and change. A consultant hired to assess the company's organizational Culture finds that only 15% of employees are open to new ideas and approaches toward Their work. Consequently the company conducts a program for employees in order to Reinforce the new corporate philosophy. After the program is completed, employees are Surveyed to see if a greater percentage is now open to innovativeness and change. Suppose that based on the sample results the company rejects the null hypothesis when in Fact it is true. Which of the following statements is correct?

Identify the type of test. -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. Which of the following Statement is true about this hypothesis test?

Write the hypotheses. -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 correct null and Alternative hypotheses are A. $H _ { 0 } : \mu = 77$ and $H _ { A } : \mu > 77$ B. $H _ { 0 } : \mu = 77$ and $H _ { A } : \mu < 77$ C. $H _ { 0 } : \mu = 77$ and $H _ { A } : \mu \neq 77$ D. $H _ { 0 } : p = 77$ and $H _ { A } : p > 77$ E. $H _ { 0 } : p = 15$ and $H _ { A } : p < 77$

Calculate the appropriate test statistic. -A report on the U.S. economy indicates that 28% of Americans have experienced Difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty. Does this indicate that the Problem is more severe among these cities? The correct value of the test statistic for Testing this claim is A. $z = - 1.28$ B. $z = - 2.67$ C. $z = 2.67$ D. $z = 1.96$ E. $z = - 1.28$

Calculate the appropriate test statistic. -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 yields a mean of 16.6 Hours and a standard deviation of 2.22 hours. The correct value of the test statistic for the Appropriate hypothesis test is A. $t = 3.532$ B. $t = - 3.532$ C. $t = 1.223$ D. $t = - 1.223$ E. $t = 0.789$

Make conclusions about the hypotheses. -A company manufacturing computer chips finds that 8% of all chips manufactured are Defective. In an effort to decrease the percentage of defective chips, management decides To provide additional training to those employees hired within the last year. After Training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis Test is performed to determine if the additional training was effective in lowering the Defect rate. Suppose the P-value associated with the test statistic is 0.0594. At α = .01,

Make conclusions about the hypotheses. -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 yields a mean of 16.6 hours and a standard deviation Of 2.22 hours. The P-value associated with the resulting test statistic is 0.0009. At α = 0.05, which of the following is the correct conclusion?

Calculate the appropriate test statistic. -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 20 of their recently paid policies. 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?

Write the hypotheses. -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. The correct null and alternative hypotheses to test the belief of Top management are A. $H _ { 0 } : \mu = 15$ and $H _ { A } : \mu < 15$ B. $H _ { 0 } : \mu = 15$ and $H _ { A } : \mu > 15$ C. $H _ { 0 } : \mu = 15$ and $H _ { A } : \mu \neq 15$ D. $H _ { 0 } : \mu \neq 15$ and $H _ { A } : \mu = 15$ E. $H _ { 0 } : \mu < 15$ and $H _ { A } : \mu > 15$

Calculate the appropriate test statistic. -A company manufacturing computer chips finds that 8% of all chips manufactured are Defective. In an effort to decrease the percentage of defective chips, management decides To provide additional training to those employees hired within the last year. After Training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis Test is performed to determine if the additional training was effective in lowering the Defect rate. The correct value of the test statistic is A. $z = - 1.56$ B. $z = - 2.57$ C. $z = 1.56$ D. $z = 1.96$ E. $z = - 2.57$