Exam 14: Hypothesis Testing: Comparing Two Populations

Which of the following is a required condition for using the normal approximation to the binomial distribution in testing the difference between two population proportions?

The test statistic to test the difference between two population proportions is the Z test statistic, which requires that the sample sizes are each sufficiently large.

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.

In testing the hypotheses: H₀: $\mu$ ₁ - $\mu$ ₂ = 0 H_A: $\mu$ ₁ - $\mu$ ₂ > 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. What conclusion can we draw at the 10% significance level?

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 sect or 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?

The Z test statistic is used to test for the difference in population means when the population variances are known.

A sample of size 100 selected from one population has 53 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:

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:

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. Estimate with 90% confidence the difference between the two population proportions.

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 Interstate 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 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.

A course coordinator at a university wants to investigate if there is a significant difference in the average final mark of students taking the same university subject in semester 1 or semester 2. A random sample of 30 students is taken from semester 1, with the average final mark is found to be 60% and the standard deviation is 5%. A random sample of 50 students is taken from semester 2, with the average final mark is 57% and the standard deviation is 4%. Assuming that the population variances are equal, is there significant evidence that the population average final mark in this course differs between semester 1 and semester 2. Test at the 5% level of significance.

When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population means, but your statistical software provides only a one-tail area of 0.028 as part of its output. The p-value for this test will be:

Testing for the equality of two population means is the same as testing for the difference between two population means.

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?

The managing director of a breakfast cereal manufacturer claims that families in which both spouses work are much more likely to be consumers of his product than those with only one working spouse. To prove his point, he commissions a survey of 300 families in which both spouses work and 300 families with only one working spouse. Each family is asked whether the company's cereal is eaten for breakfast. The results are shown below. Two spouses working One spouse working Eat cereal 114 87 Don't eat cereal 186 213 Use the p-value method to test the managing director's claim, at a 5% significance level of significance.

When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population proportions. The two sample proportions are p₁ = 0.25 and p₂ = 0.20 and the standard error of the sampling distribution of $p _ { 1 } - p _ { 2 }$ is 0.04. The calculated value of the test statistic will be:

The pooled proportion estimate is used to estimate the standard error of the difference between two proportions when the proportions of two populations are hypothesized to be equal.

A psychologist has performed the following experiment. For each of 10 sets of identical twins who were born 30 years ago, she recorded their annual incomes according to which twin was born first. The results (in $000) are shown below. Twin set First born Second born 1 32 44 2 36 43 3 21 28 4 30 39 5 49 51 6 27 25 7 39 32 8 38 42 9 56 64 10 44 44 Can she infer at the 5% significance level that there is a difference in income between the twins?

A quality control inspector keeps a tally sheet of the numbers of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Production line Acceptable products Unacceptable products 1 152 48 2 136 54 Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?