Exam 14: Hypothesis Testing: Comparing Two Populations

The following data were generated from a matched pairs experiment: Pair: 1 2 3 4 5 6 7 Sample 1: 8 15 7 9 10 13 11 Sample 2: 12 18 8 9 12 11 10 Determine whether these data are sufficient to infer at the 10% significance level that the two population means differ.

A sample of size 100 selected from one population has 60 successes, and a sample of size 150 selected from a second population has 95 successes. The test statistic for testing the equality of the population proportions is equal to:

In testing the hypotheses: H₀: p₁ - p₂ = 0.10 H₁: p₁ - p₂ ≠ 0.10, we found the following statistics: n₁ = 350, x₁ = 178. n₂ = 250, x₂ = 112. What conclusion can we draw at the 5% significance level?

For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:

An industrial statistician wants to determine whether efforts to promote safety have been successful. By checking the records of 250 employees, he finds that 30 of them have suffered either minor or major injuries that year. A random sample of 400 employees taken in the previous year revealed that 80 had suffered some form of injury. a. Can the statistician infer at the 5% significance level that efforts to promote safety have been successful? b. What is the p-value of the test?

Two independent samples of sizes 30 and 40 are randomly selected from two populations to test the difference between the population means, µ $\mu$ ₂ - µ $\mu$ _1, where the population variances are unknown. Which of the following best describes the sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ ?

In order to test the hypotheses: H₀: µ $\mu$ ₁ - µ $\mu$ ₂ = 0 H₁: µ $\mu$ ₁ - µ $\mu$ ₂ ? $\neq$ 0, we independently draw a random sample of 18 observations from a normal population with standard deviation of 15, and another random sample of 12 from a second normal population with standard deviation of 25. a. If we set the level of significance at 5%, determine the power of the test when $\mu$ ₁ - $\mu$ ₂ = 5. b. Describe the effect of reducing the level of significance on the power of the test.

A t test for testing the difference between two population means from two independent samples is the same as the t test to test the difference of two population means in a matched pairs experiment.

A survey of 1500 Queenslanders reveals that 945 believe there is too much violence on television. In a survey of 1500 Western Australians, 810 believe that there is too much television violence. Can we infer at the 99% significance level that the proportions of Queenslanders and Western Australians who believe that there is too much violence on television differ?

In testing the difference between the means of two normal populations with known population standard deviations the test statistic calculated from two independent random samples equals 2.56. If the test is two-tailed and the 1% level of significance has been specified, the conclusion should be:

We can design a matched pairs experiment when the data collected are:

Thirty-five employees who completed two years of tertiary education were asked to take a basic mathematics test. The mean and standard deviation of their marks were 75.1 and 12.8, respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test marks were 72.1 and 14.6, respectively. a. Estimate with 90% confidence the difference in mean scores between the two groups of employees. b. Explain how to use the interval estimate in part a. to test the hypotheses.

When testing for the difference between two population means and the population variances are unknown, a t test is used.

Two independent samples of sizes 40 and 50 are randomly selected from two normally distributed populations. Assume that the population variances are known. In order to test the difference between the population means, µ $\mu$ ₁ - µF $\mu$ ₂, which of the following test statistics should be used?

A marketing consultant is studying the perceptions of married couples concerning their weekly food expenditures. He believes that the husband's perception would be higher than the wife's. To judge his belief, he takes a random sample of 10 married couples and asks each spouse to estimate the family food expenditure (in dollars) during the previous week. The data are shown below. Couple Husband Wife 1 380 270 2 280 300 3 215 185 4 350 320 5 210 180 6 410 390 7 250 250 8 360 320 9 180 170 10 400 330 Can the consultant conclude at the 5% significance level that the husband's estimate is higher than the wife's estimate?

In testing the hypotheses: H₀: $\mu$ ₁ - $\mu$ ₂ = 0 H_A: $\mu$ ₁ - $\mu$ ₂ $\neq$ 0, two random samples from two normal populations produced the following statistics: n₁ = 51, x₁-bar = 35, s₁ = 28. n₂ = 40, x₂-bar = 28, s₂ = 10. Assume that the two population variances are different. a. Estimate with 95% confidence the difference between the two population means. b. Explain how to use this confidence interval for testing the hypotheses.

In testing the hypotheses H₀: p₁ - p₂ = 0 H_A: p₁ - p₂ ≠ 0, we find the following statistics: n₁ = 400, x₁ = 105. n₂ = 500, x₂ = 140. What conclusion can we draw at the 10% significance level?

In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows: n₁ = 25, $\bar { x } _ { 1 }$ = 7.30, s₁ = 1.05. N₂ = 30, $\bar { x } _ { 2 }$ = 6.80, s₂ = 1.20. Assume that the population variances are equal. Then the standard error of the sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ is equal to:

A management consultant wants to compare the incomes of graduates of MBA programs with those of graduates with Bachelor's degrees. In a random sample of the incomes of 20 people taken five years after they received their MBAs, the consultant found the mean salary and the standard deviation to be $45 300 and $9600, respectively. A random sample of the incomes of 25 people taken five years after they received their Bachelor's degrees yielded a mean salary of $43 600 with a standard deviation of $12 300. Can we infer at the 10% level of significance that the population means differ?

In testing the hypotheses: H₀: p₁ - p₂ = 0 H₁: p₁ - p₂ > 0, we find the following statistics: n₁ = 200, x₁ = 80. n₂ = 200, x₂ = 140. a. What is the p-value of the test? b. What is the conclusion if tested at a 5% significance level? c. Estimate with 95% confidence the difference between the two population proportions.