Exam 10: Hypothesis Testing: Two-Sample Tests

Instruction 10-12 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. -Referring to Instruction 10-12,what is/are the critical value(s)when testing whether population proportions are different if α = 0.10?

The Sydney Morning Herald recently published an article describing differences in perception of sexual harassment on the job between men and women.The article claimed that women perceived the problem to be much more prevalent than did men.One question asked to both men and women was: "Do you think sexual harassment is a major problem in the Australian workplace?" 24% of the men responded "Yes," compared to 62% of the women.Suppose that 150 women and 200 men were interviewed.Construct a 95% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the Australian workplace.

Instruction 10-14 A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2", perform the appropriate test at a level of significance of 0.01. -Referring to Instruction 10-14,the null hypothesis will be rejected if the test statistic is _______.

Instruction 10-12 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. -Referring to Instruction 10-12,what is/are the critical value(s)when performing a Z test on whether population proportions are different if α = 0.05?

When performing a two-tailed test,the lower-tailed critical value of the F distribution with n₁ - 1 degrees of freedom in the numerator and n₂ - 1 degrees of freedom in the denominator is exactly equivalent to the reciprocal of the upper-tailed critical value of the F distribution with n₂ - 1 degrees of freedom in the numerator and n₁ - 1 degrees of freedom in the denominator.

In testing for differences between the means of two related populations,the null hypothesis is

Instruction 10-10 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting students and 52 economics students had job offers. If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2", perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Instruction 10-13,the null hypothesis will be rejected if the test statistic is _______.

Instruction 10-2 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below. Hypothesised Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean 48266.7 Sample Standard Deviation 13577.63 Population 2 Sample Sample Size 12 Sample Mean 55000 Sample StandardDeviation 11741.29 Differencein Sample Means -6733.3 t -Test Statistic -1.40193 Lower-Tail Test Lower Critical Value -1.70113 p-Value 0.085962 -Referring to Instruction 10-2,what is the 95% confidence interval estimate for the difference between two means?

The Sydney Morning Herald recently published an article describing differences in perception of sexual harassment on the job between men and women.The article claimed that women perceived the problem to be much more prevalent than did men.One question asked to both men and women was: "Do you think sexual harassment is a major problem in the Australian workplace?" 24% of the men responded "Yes," compared to 62% of the women.Suppose that 150 women and 200 men were interviewed.Construct a 90% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the Australian workplace.

Instruction 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: $\quad \bar { X } _ { G } = 35$ months, $S _ { G } { } ^ { 2 } = 900$ Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$ -Referring to Instruction 10-3,which of the following represents the relevant hypotheses tested by the real estate company?

Moving companies are required by the government to publish a Carrier Performance Report each year.One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed.Suppose two companies,Econo-Move and On-the-Move,each decide to estimate this figure by sampling their records,and they report the data shown in the following table. Econo-Move On-the-Move Total shipments sampled 900 750 Number of shipments with a claim \geq\ 50 162 60 The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed.Which test would be used to properly analyse the data in this experiment?

Instruction 10-7 To investigate the efficacy of a diet, a random sample of 16 male patients is drawn from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 kilograms with the standard deviation of differences computed as 6.0 kilograms. -Referring to Instruction 10-7,the computed t statistic is__________.

The test for the equality of two population variances is based on

Instruction 10-2 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below. Hypothesised Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean 48266.7 Sample Standard Deviation 13577.63 Population 2 Sample Sample Size 12 Sample Mean 55000 Sample StandardDeviation 11741.29 Differencein Sample Means -6733.3 t -Test Statistic -1.40193 Lower-Tail Test Lower Critical Value -1.70113 p-Value 0.085962 -Referring to Instruction 10-2,what is the 90% confidence interval estimate for the difference between two means?

Instruction 10-4 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Student Exam Score Before Course Exam Score After Course (2) (1) 1 530 670 2 650 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Instruction 10-4,one must assume that the population of difference scores is normally distributed.

Instruction 10-7 To investigate the efficacy of a diet, a random sample of 16 male patients is drawn from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 kilograms with the standard deviation of differences computed as 6.0 kilograms. -Referring to Instruction 10-7,the critical value for a one-tailed test of the null hypothesis of no difference at the $\alpha$ = 0.05 level of significance is __________.

Instruction 10-14 A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2", perform the appropriate test at a level of significance of 0.01. -Referring to Instruction 10-14,the value of the test statistic is _______.

A test for the difference between the means of two populations that have a common characteristic is known as the__________for the mean difference in related populations.

In most cases the population standard deviation is unknown.

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is