Exam 9: B: large-Sample Tests of 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 practical consequences for the Liberal party opponent if he makes a Type II error.

Defective Toasters Narrative A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept. -Refer to Defective Toasters Narrative. Describe the Type II error for this .

Insurance Policy Sales Narrative Independent random samples of and sales phone calls for an insurance policy were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 80 successful sales, and sample 2 had 88 successful sales. -Refer to Insurance Policy Sales Narrative. p-value approach: Find the p-value for the test. Test for a significant difference in the population means at the 1% significance level.

Develop the null and appropriate hypotheses that are most appropriate for each of the following situations: a. A meteorologist claims that the average high temperature for the month of August in Montreal is 27°C. If the residents of Montreal do not believe this to be true, what hypotheses should they test? b. A car manufacturing plant is acting in accordance with the public's interest in making cars that have fuel consumption of at most 8.2 litres per 100 km. The supervisor will let the cars off the manufacturing floor only if the fuel consumption is less than 8.8 L/100 km. What hypotheses should the plant test? c. A spokesperson for the Health Department reports that a fish is unsafe for human consumption if the polychlorinated biphenyl (PCB) concentration exceeds 5 ppb. The Carlson family is interested in the mean PCB concentration in a fish from the lake on which they live. What hypotheses should they test? d. An Internet survey revealed that 50% of Internet users received more than 10 email messages per day. A similar study on the use of email was repeated. The purpose of the study was to see whether use of email has increased.

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. Find the p-value for this test.

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 p-value for the test in the previous question.

Medical Instruments Narrative In testing the hypotheses vs. , the following statistics were obtained: , , , and , where and represent the number of defective components found in medical instruments in the two samples. -Refer to Medical Instruments Narrative. What is the p-value of the test? Briefly explain how to use the p-value for testing the hypotheses.

Allergy Drug Narrative In clinical studies of an allergy drug, 81 of the 900 subjects experienced drowsiness. A competitor claims that 10% of the users of this drug experience drowsiness. -Refer to Allergy Drug Narrative. Is there enough evidence at the 5% significance level to infer that the competitor is correct? Justify your conclusion.

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. Construct a 95% confidence interval for the difference in mean amount of life insurance held by professional men and women.

Gas Heat Narrative A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.65. A sample of 75 homes was selected and it was found that 44 of them heat with gas. -Refer to Gas Heat Narrative. Find the p-value for this test.

Allergy Drug Narrative In clinical studies of an allergy drug, 81 of the 900 subjects experienced drowsiness. A competitor claims that 10% of the users of this drug experience drowsiness. -Refer to Allergy Drug Narrative. Explain how to use this confidence interval to test the hypotheses.

Catalogue Mail-Orders Narrative A mail-order catalogue claims that customers will receive their product within four days of ordering. A competitor believes that this claim is an underestimate. -Refer to Catalogue Mail-Orders Narrative. Describe the Type II error for this .

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 practical consequences for the Liberal party opponent if he makes a Type I error.

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. If you planned to conduct your test using what would be your test conclusions?

Defective Toasters Narrative A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept. -Refer to Defective Toasters Narrative. Describe the Type I error.

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. Compute the value of the test statistic.

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. Explain how to use the 95% confidence interval for to test the appropriate hypotheses at = 0.05.

Tennis Magazine Narrative A marketing manager wants to test the hypothesis that 90% of Tennis magazine's subscribers are homeowners. Accordingly, a simple random sample of 80 is taken from the magazine's list of subscribers. The sample turns out to contain 64 homeowners. Use a significance level of = 0.05. -Refer to Tennis Magazine Narrative. State the appropriate hypotheses.

Gas Heat Narrative A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.65. A sample of 75 homes was selected and it was found that 44 of them heat with gas. -Refer to Gas Heat Narrative. Perform the appropriate test of hypothesis to determine whether the proportion of homes heated by gas has changed. Test using $\alpha$ = 0.05.

Defective Toasters Narrative A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept. -Refer to Defective Toasters Narrative. From the manufacturer's point of view, which error would be the more serious? Justify your answer.