Exam 9: B: large-Sample Tests of Hypotheses

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. Compute the p-value for the test.

Drug Testing Narrative An experiment was conducted to test the effect of a new drug on a viral infection. The infection was induced in 100 mice, and the mice were randomly split into 2 groups of 50. The first group, the control group, received no treatment for the infection. The second group received the drug. The proportions of survivors, and in the 2 groups after a 30-day period, were found to be 0.40 and 0.64, respectively. -Refer to Drug Testing Narrative. Is Use a 95% confidence interval to estimate the actual difference in the cure rates for the treated versus the control groups.

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. Calculate the value of the test statistic.

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 pooled estimate of the common proportion p.

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 I 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. Calculate the standard error of the difference in the two sample proportions Make sure to use the pooled estimate for the common value of p.

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. Critical value approach: Find the rejection region when Do the data provide sufficient evidence to indicate a difference in the population proportions?

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. What is your conclusion?

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. Compute the p-value of the test.

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. Find a 99% lower confidence bound for the difference in the average per capita beef consumption for the two groups. Does your confidence bound confirm your conclusions in the previous question? Explain. What additional information does the confidence bound give you?

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. State the appropriate null and alternative hypotheses to be tested by the competitor.

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. Suppose you have no preconceived theory concerning which parameter, or is the larger and you wish to detect only a difference between the two parameters if one exists. What should you choose as the null and alternative hypotheses for a statistical test?

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. State the appropriate null and alternative hypotheses.

Medical School Completion Narrative A university investigation was conducted to determine whether women and men complete medical school in significantly different amounts of time, on the average. Two independent random samples were selected and the following summary information concerning times to completion of medical school computed: -Refer to Medical School Completion Narrative. Find the p-value associated with the test in the previous question.

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. State the appropriate null and alternative hypotheses to be tested by the manufacturer.

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: -Independent random samples of 35 and 50 observations are drawn from two quantitative populations, 1 and 2, respectively. The sample data summary is shown here: Do the data present sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2? Use the p-value approach and the critical value approach and explain your conclusion.

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. State the appropriate null and alternative hypotheses to be tested by the Liberal party opponent .

Transport Quebec repaired hundreds of bridges in 1993. To check the average cost to repair a bridge, a random sample of n = 55 bridges was chosen. The mean and standard deviation for the sample are $25,788 and $1540, respectively. Records from previous years indicate an average bridge repair cost was $25,003. Use the sample data to test that the 1993 mean $\mu$ is greater than $25,003. Use $\alpha$ = 0.05.

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. Interpret and explain how to use the confidence interval to test the hypotheses.

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 null and alternative hypotheses.