Exam 13: Hypothesis Testing: Comparing Two Populations

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:

In testing the hypotheses: H₀: 1 - 2 = 0 H_A: 1 - 2 > 0, two random samples from two normal populations produced the following statistics: n₁ = 51, $\bar { X } _ { 1 }$ = 35, s1 = 28. n₂ = 40, $\bar { X } _ { 2 }$ = 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:

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 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?

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?

Which of the following best describes the symbol $\bar { X } _ { D }$ ?

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

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 What is the p-value of the test?

In testing the hypotheses: H0: D = 5 HA: D  5, two random samples from two normal populations produced the following statistics: nD = 36, $\bar { X } _ { D }$ = 7.8, sD = 7.5. What conclusion can we draw at the 5% significance level?

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?

When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population proportions. If the value of the test statistic Z is 2.05, then the p-value is:

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:

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

In testing the hypotheses: H0: p1 - p2 = 0 HA: p1 - p2 > 0, we find the following statistics: n1 = 200, x1 = 80. n2 = 400, x2 = 140. a. What is the p-value of the test? b. What is the conclusion if tested at a 5% significance level?

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?

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?

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.

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.

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