Exam 9: Inferences From Two Samples

Assume that you plan to use a significance level of $\alpha = 0.05$ to test the claim that $p _ { 1 } = p _ { 2 }$ . Use the given sample sizes and numbers of successes to find the pooled estimate $\bar { p }$ . Round your answer to the nearest thousandth. =677 =3377 =172 =654

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { d } = 0$ . Compute the value of the $t$ test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. x 28 31 20 25 28 27 33 35 y 26 27 26 25 29 32 33 34

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { d } = 0$ . Compute the value of the $t$ test statistics. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. x 9 6 7 5 12 y 6 8 3 6 7

When testing the claim that $p _ { 1 } = p _ { 2 }$ , a test statistic of $z = 2.04$ is obtained. Find the $P$ -value obtained from this test statistic.

Test the indicated claim about the variances or standard deviations of two populations. that both samples are independent simple random samples from populations having normal distributions. When 25 randomly selected customers enter any one of several waiting lines, their waiting times have a standard deviation of 5.35 minutes. When 16 randomly selected customers enter a single main waiting line, their waiting times have a standard deviation of 2.2 minutes. Use a 0.05 significance level to test the claim that there is more variation in the waiting times when several lines are used. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.

A researcher wishes to determine whether the blood pressure of vegetarians is, on average, lower than the blood pressure of nonvegetarians. Independent simple random samples of 85 vegetarians and 75 nonvegetarians yielded the following sample statistics for systolic blood pressure: Vegetarians Nonvegetarians =85 =75 =124.1 =138.7 =38.7 =39.2 Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of vegetarians is lower than the mean systolic blood pressure of nonvegetarians. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.

Determine whether the samples are dependent or independent. The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and After drug treatment. The data consist of before and after intensities for each patient.

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that mothers spend more time (in minutes) Driving their kids to activities than fathers do?

In a random sample of 300 women, $45 \%$ favored stricter DUI legislation. In a random sample of 200 men, $25 \%$ favored stricter DUI legislation. Construct a $95 \%$ confidence interval for the difference between the population proportions $p _ { 1 } - p _ { 2 }$ . Assume that the samples are independent and that they have been randomly selected.

Determine whether the samples are independent or dependent. The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug Treatment. The data consist of before and after intensities for each patient.

Assume that the following confidence interval for the difference in the mean time (in minutes) for male students to complete a statistics test (sample 1) and the mean time for female students to complete a statistics test (sample 2) was constructed using independent simple random samples. $- 0.2$ minutes $< \mu _ { 1 } - \mu _ { 2 } < 2.7$ minutes What does the confidence interval suggest about the difference in length between male and female test completion times?

Test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores were recorded before and after the training. The results are shown below. Subject A B C D E F G Before 9.5 9.4 9.6 9.5 9.5 9.6 9.7 After 9.6 9.6 9.6 9.4 9.6 9.9 9.5 Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnasts' scores. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal $\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$ , so that the standard error of the difference between means is obtained by pooling the sample variances. A paint manufacturer wanted to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B =71.5 =68.5 =3.4 =3.6 =11 =9 Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A and the mean drying time for paint type B.

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A paint manufacturer wished to compare the drying times of two different types of paint .Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B =75.7 =64.3 =4.5 =5.1 =11 =9 Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A and the mean drying time for paint type B.

Express the alternative hypothesis in symbolic form. An automobile technician claims that the mean amount of time (in hours)per domestic car repair is more than that of foreign cars. Assume that two samples are independent. Let the domestic car repair times be the first Population and the foreign car repair times be the second population.

Suppose you wish to test a claim about the mean of the differences from dependent samples or to construct a confidence interval estimate of the mean of the differences from dependent samples. What are the requirements?

If the heights of male college basketball players and female basketball players are used to construct a $95 \%$ confidence interval for the difference between the two population means, the result is $15.35 \mathrm {~cm} < \mu _ { 1 } - \mu _ { 2 } < 19.81 \mathrm {~cm}$ , where heights of male players correspond to population 1 and heights of female players correspond to population 2 . Express the confidence interval with heights of female basketball players being population 1 and heights of male basketball players being population 2 .

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth. A 69 66 61 63 51 B 25 23 20 25 22

Construct a confidence interval for $\mu _ { d }$ , the mean of the differences $d$ for the population of paired data. Assume that the population of paired differences is normally distributed. A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a $99 \%$ confidence interval for the mean difference between the before and after scores. Before 70 80 92 99 93 97 76 63 68 71 74 After 69 79 90 96 91 95 75 64 62 64 76

A researcher wishes to compare how students at two different schools perform on a math test? He randomly selects 40 students from each school and obtains their test scores. He pairs the first score from school A with the first school from school B, the second score from school A with the second school from school B and so on. He then performs a hypothesis test for matched pairs. Is this approach valid? Why or why not? If it is not valid, how should the researcher have proceeded?