Exam 9: B: large-Sample Tests of Hypotheses

Average Childcare Costs Narrative The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40. -Refer to Average Childcare Costs Narrative. Find the power of the test when is actually $685 and = 0.05. Interpret the results.

Soap Sales Narrative In testing the hypotheses vs. , use the following statistics: , , , and , where and represent the number of Dial Soap sales in the two samples, respectively. -Refer to Soap Sales Narrative. Explain how to use the p-value to test the hypotheses.

Federal Votes Narrative A Conservative party candidate in a federal election believes that 54% of Canadian voters are supporting him. His Liberal party opponentbelieves this estimate is too high. -Refer to Federal Votes Narrative. Describe the Type II error for this .

Laptop Battery Time Narrative The manufacturer of a particular battery pack for laptop computers claims its battery pack can function for eight hours, on average, before having to be recharged. A random sample of 36 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.9 hours. -Refer to Laptop Battery Time Narrative. A competitor claims that the manufacturer's claim is too high. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using = 0.05.

Refer to Plant Experiments Narrative. What hypothesis should you use to test the geneticist's claim?

Nuclear Weapons Freeze Narrative A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze. -Refer to Nuclear Weapons Freeze Narrative. State and interpret your conclusion.

Average Daily Wages Narrative The daily wages in a particular industry are normally distributed with a mean of $60 and a standard deviation of $13. Suppose a company in this industry employs 50 workers and pays them $57.5 on the average. Based on this sample mean, can these workers be viewed as a random sample from among all workers in the industry? -Refer to Average Daily Wages Narrative. Find the p-value for the test.

Laptop Battery Charge Time Narrative A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information: -Refer to Laptop Battery Charge Time Narrative. Find the p-value for the test in the previous question.

Red Meat Consumption Narrative To test the theory that the consumption of red meat in Canada has decreased over the past 10 years, a researcher decides to select hospital nutrition records for 400 subjects surveyed 10 years ago and to compare their average amount of beef consumed per year to amounts consumed by an equal number of subjects interviewed this year. The data are given in the table. -Refer to Red Meat Consumption Narrative. Do the data present sufficient evidence to indicate that per capita beef consumption has decreased in the past 10 years? Test at the 1% level of significance.

Life Insurance Narrative An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000. -The proportion of defective computers built by Byte Computer Corporation is 0.15. In an attempt to lower the defective rate, the owner ordered some changes made in the assembly process. After the changes were put into effect, a random sample of 42 computers was tested, revealing a total of 4 defective computers. Perform the appropriate test of hypothesis to determine whether the proportion of defective computer has been lowered. Use $\alpha$ = 0.01.

Business Graduates Earnings Narrative A professor claims that 70% of business graduates earn more than $45,000 per year. In a random sample of 300 graduates, 195 earn more than $45,000. -Refer to Business Graduates Earnings Narrative. State the appropriate null and hypotheses.

Cable Narrative A cable company in Ontario is thinking of offering its service in one of two cities: Guelph and Kitchener. Allegedly, there is a proportion of households in either city ready to be hooked up to the cable, but the company wants to test the claim. Accordingly, it takes a simple random sample in each city. In Guelph, 175 of 200 households say they will join. In Kitchener, 665 of 800 households say the same. -Refer to Cable Narrative. Calculate the p-value and write your conclusion given that = 0.05.

Life Insurance Narrative An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000. -Refer to Life Insurance Narrative. Calculate the p-value.

Union Contract Narrative A union composed of several thousand employees is preparing to vote on a new contract. A random sample of 500 employees yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes. -Refer to Union Contract Narrative. Compute the p-value for the test.

Cable Narrative A cable company in Ontario is thinking of offering its service in one of two cities: Guelph and Kitchener. Allegedly, there is a proportion of households in either city ready to be hooked up to the cable, but the company wants to test the claim. Accordingly, it takes a simple random sample in each city. In Guelph, 175 of 200 households say they will join. In Kitchener, 665 of 800 households say the same. -Refer to Cable Narrative. Calculate the value of the test statistic.

Average Childcare Costs Narrative The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40. -An Internet server claimed that its users averaged 15 hours per week. To determine whether this was an overstatement, a competitor conducted a survey of 150 customers and found that the average time spent online was 13 hours per week with a standard deviation of 6.5 hours. Do the data provide sufficient evidence to indicate that the average hours of use are less than that claimed by the first Internet server? Test at the 1% level of significance.

Nuclear Weapons Freeze Narrative A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze. -Refer to Environment Canada Project Narrative. Set up the appropriate rejection region for $\alpha$ = 0.01.

Cable Narrative A cable company in Ontario is thinking of offering its service in one of two cities: Guelph and Kitchener. Allegedly, there is a proportion of households in either city ready to be hooked up to the cable, but the company wants to test the claim. Accordingly, it takes a simple random sample in each city. In Guelph, 175 of 200 households say they will join. In Kitchener, 665 of 800 households say the same. -Refer to Cable Narrative. Construct a 95% confidence interval for the difference in proportions of households in Guelph and Kitchener that are ready to hook up to the cable.

Cable Narrative A cable company in Ontario is thinking of offering its service in one of two cities: Guelph and Kitchener. Allegedly, there is a proportion of households in either city ready to be hooked up to the cable, but the company wants to test the claim. Accordingly, it takes a simple random sample in each city. In Guelph, 175 of 200 households say they will join. In Kitchener, 665 of 800 households say the same. -Refer to Cable Narrative. Calculate the standard error of .

Copper Pipes Narrative A manufacturer of copper pipes must produce pipes with a diameter of precisely 5 cm. The firm's quality inspector wants to test the hypothesis that pipes of the proper size are being produced. Accordingly, a simple random sample of 100 pipes is taken from the production process. The sample mean diameter turns out to be 4.98 cm and the sample standard deviation 0.2 cm. Using a significance level of = 0.05, test the appropriate hypotheses. -Refer to Copper Pipes Narrative. Calculate the p-value and write your conclusion.