Exam 14: Hypothesis Testing: Comparing Two Populations

Motor vehicle insurance appraisers examine cars that have been involved in accidental collisions to assess the cost of repairs. An insurance executive is concerned that different appraisers produce significantly different assessments. In an experiment, 10 cars that had recently been involved in accidents were shown to two appraisers. Each assessed the estimated repair costs. The results are shown below. Car Appraiser 1 Appraiser 2 1 1650 1400 2 360 380 3 640 600 4 1010 920 5 890 930 6 750 650 7 440 410 8 1210 1080 9 520 480 10 690 770 Can the executive conclude at the 5% significance level that the appraisers differ in their assessments?

In testing the difference between the means of two normal populations, using two independent samples, when the population variances are unknown and unequal, the sampling distribution of the resulting statistic is: A. normal. B. Student t C. approximately normal. D. approximately Student t.

In testing the difference between two population means, for which the population variances are unknown and are not assumed to be equal, two independent samples of large sizes are drawn from the populations. Which of the following tests is appropriate? A. Z-test. B. Pooled-variances t -test. C. Unequal variances t -test. D. Matched pars t -test.

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

A simple random sample of ten firms was asked how much money (in thousands of dollars) they spent on employee training programs this year and how much they plan to spend on these programs next year. The data are shown below. Firm 1 2 3 4 5 6 7 8 9 10 This year 25 31 12 15 21 36 18 5 9 17 Next year 21 30 18 20 22 36 20 10 8 15 Assume that the populations of amount spent on employee training programs are normally distributed. a. Estimate with 95% confidence the mean difference. b. Briefly explain what the interval estimate in part a. tells you.

In a matched pairs experiment, when testing for the difference between two means, the value of µ_D is obtained by subtracting the first sample mean from the second sample mean.

A simple random sample of ten firms was asked how much money (in thousands of dollars) they spent on employee training programs this year and how much they plan to spend on these programs next year. The data are shown below. Firm 1 2 3 4 5 6 7 8 9 10 This year 25 31 12 15 21 36 18 5 9 17 Next year 21 30 18 20 22 36 20 10 8 15 Assume that the populations of amount spent on employee training programs are normally distributed. Can we infer at the 5% significance level that more money will be spent on employee training programs next year than this year?

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. What conclusion can we draw at the 10% significance level?

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.

Do government employees take longer tea breaks than private-sector workers? That is the question that interested a management consultant. To examine the issue, he took a random sample of nine government employees and another random sample of nine private-sector workers and measured the amount of time (in minutes) they spent in tea breaks during the day. The results are listed below. Government employees Private sector workers 23 25 18 19 34 18 31 22 28 28 33 25 25 21 27 21 32 30 Do these data provide sufficient evidence at the 5% significance level to answer the consultant's question in the affirmative?

Ten functionally illiterate adults were given an experimental one-week crash course in reading. Each of the 10 was given a reading test prior to the course and another test after the course. The results are shown below. Adult 1 2 3 4 5 6 7 8 9 10 Score after course 48 42 43 34 50 30 43 38 41 3 Score before course 31 34 18 30 44 28 34 33 27 32 Is there enough evidence to infer at the 5% significance level that the reading scores have improved?

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: A. populations are normally distributed. B. sample sizes are small. C. samples are independently drawn from the populations. D. null hypothesis states that the two population proportions are equal.

A political analyst in Perth surveys a random sample of Labor Party members and compares the results with those obtained from a random sample of Liberal Party members. This would be an example of: A. independent samples. B. dependent samples. C. independent samples only if the sample sizes are equal. D. dependent samples only if the sample sizes are equal.

In testing the hypotheses: H₀: p₁ - p₂ = 0.10 H₁ : p₁ - p₂ $\neq$ 0.10, we find the following statistics: n₁ = 150, x₁ = 72. n₂ = 175, x₂ = 70. What conclusion can we draw at the 5% significance level?

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?

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: A. to reject the null hypothesis. B. not to reject the null hypothesis. C. the test is inconclusive. D. None of these choices are correct.

In testing the difference between two population means, using two independent samples, the sampling distribution of the sample mean difference $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ is normal if the: A. sample sizes are both greater than 30 . B. popul ations are normal. C. populations are non-normal and the sample sizes are large. D. All of these choices are correct.

Do interstate drivers exceed the speed limit more frequently than local motorists? This vital question was addressed by the Road Traffic Authority. A random sample of the speeds of 2500 randomly selected cars was categorised according to whether the car was registered in the state or in some other state, and whether or not the car was violating the speed limit. The data are shown below. Local cars Inter state cars Speeding 521 328 Not speeding 1141 510 Do these data provide enough evidence to support the highway patrol's claim at the 5% significance level?

A politician has commissioned a survey of blue-collar and white-collar employees in her electorate. The survey reveals that 286 out of 542 blue-collar workers intend to vote for her in the next election, whereas 428 out of 955 white-collar workers intend to vote for her. a. Can she infer at the 5% level of significance that the level of support differs between the two groups of workers? b. What is the p-value of the test? Explain how to use it to test the hypotheses.

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 40 pairs, is: A. 38. B. 39. C. 1. D. 2.