Exam 14: Hypothesis Testing: Comparing Two Populations

A university lecturer claims that students who attend lecturers score a higher final mark in her course than students who watch the lecture recordings online. The lecturer takes a random sample of the final marks of 40 students who attended her university lectures and found their average mark was 65% with a standard deviation of 5%. The lecturer takes a random sample of 30 university students who watched the lecture recordings online and found their average mark was 60% with a standard deviation of 8%. Is there significant evidence to support this university lecturer's claim? Test at the 5% level of significance, assuming that the population variances are unequal.

A test is being conducted to test the difference between two population means, using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the: A. normal. B. binomial. C. Student t D. F.

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as: A. matched samples. B. independent samples. C. weighted samples. D. random samples.

The degrees of freedom for a t test of the difference of population means in a matched pairs experiment is samples is n₁ - 1, because n₁ = n₂.

A sample of size 150 from population 1 has 40 successes. A sample of size 250 from population 2 has 30 successes. The value of the test statistic for testing the null hypothesis that the proportion of successes in population 1 exceeds the proportion of successes in population 2 by 0.05 is: A. 1.645 B. 2.327. C. 1.960. D. 1.977

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?

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 a. Estimate with 90% confidence the mean difference. b. Briefly describe what the interval estimate in part a. tells you, and explain how to use it to test the hypotheses.

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

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?

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.

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.

Because of the rising costs of industrial accidents, many chemical, mining and manufacturing firms have instituted safety courses. Employees are encouraged to take these courses, which are designed to heighten safety awareness. A company is trying to decide which one of two courses to institute. To help make a decision, eight employees take course 1 and another eight take course 2. Each employee takes a test, which is graded out of a possible 25. The safety test results are shown below. Course 1 14 21 17 14 17 19 20 16 Course 2 20 18 22 15 23 21 19 15 Assume that the scores are normally distributed. Does the data provide sufficient evidence at the 5% level of significance to infer that the marks from course 1 are lower than those from course 2?

The marketing manager of a pharmaceutical company believes that more females than males use its acne medicine. In a recent survey, 2500 teenagers were asked whether or not they use that particular product. The responses, categorised by gender, are summarised below. Use acne medicine Don't use acne medicine Female 540 810 Male 391 759 a. Do these data provide enough evidence at the 10% significance level to support the manager's claim? b. Estimate with 90% confidence the difference in the proportions of male and female users of the acne medicine. c. Describe what the interval estimate in part b. tells you.

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 - µ $\mu$ ₂, which of the following test statistics should be used? A. t-test B. Chi-square test C. Z-test D. None of these choices are correct.

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: A. -11.1051 B. -17.1107 C. -0.0944. D. -1.0944.

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

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?

The owner of a service station wants to determine whether the owners of new cars (two years old or less) change their cars' oil more frequently than owners of older cars (more than two years old). From his records, he takes a random sample of 10 new cars and 10 older cars and determines the number of times the oil was changed for each in the last 12 months. The data are shown below. Frequency of oil changes in the past 12 months New car owners Old car owners 6 4 3 2 3 1 3 2 4 3 3 2 6 2 5 3 5 2 4 1 Do these data allow the service station owner to infer at the 10% significance level that new car owners change their cars' oil more frequently than older car owners?

A political poll taken immediately prior to a state election reveals that 158 out of 250 male voters and 105 out of 200 female voters intend to vote for the Independent candidate. Can we infer at the 5% significance level that the proportions of male and female voters who intend to vote for the Independent candidate 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: A. -0.5319. B. 0.7293 C. -0.419. D. 0.2702.