Exam 10: Hypothesis Testing: Two Sample Tests

Instruction 10-4 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: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$ Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$ -Referring to Instruction 10-4,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?

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 Standard Deviation 11741.29 Difference in Sample Means -6733.3 -Test Statistic -1.40193 Lower-Tail Test Lower Critical Value -1.70113 p -Value 0.085962 -Referring to Instruction 10-2,what is the 99% confidence interval estimate for the difference between two means?

Instruction 10-3 The use of preservatives by food processors has become a controversial issue.Suppose two preservatives are extensively tested and determined safe for use in meats.A processor wants to compare the preservatives for their effects on retarding spoilage.Suppose 15 cuts of fresh meat are treated with preservative A and 15 are treated with preservative B,and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat.The results are summarised in the table below. PreservativeA PreservativeB =106.4 hours =96.54 hours =10.3 hours =13.4 hours -Referring to Instruction 10-3,state the test statistic for determining if the population variances differ for preservatives A and B.

Instruction 10-5 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 (1) Exam Score After Course (2) 3-3 2 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Instruction 10-5,the value of the standard error of the difference scores is

A business statistics lecturer wanted to test whether the grades on a business statistics test were the same for upper and lower students.The lecturer took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the lecturer should use a t test with independent samples.

Instruction 10-12 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Instruction 10-12,what is the 95% confidence interval estimate for the difference in the two means?

Instruction 10-9 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 10-9,what is/are the critical value(s)when performing a Z test on whether population proportions are different if α = 0.05?

The Sydney Morning Herald recently published an article indicating 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 compared to 62% of the women responded "Yes".Suppose that 150 women and 200 men were interviewed.What is the value of the test statistic?

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination.A group of 50 men (group 1)and 40 women (group 2)were asked if they thought sexual discrimination is a problem in Australia.Of those sampled,11 of the men and 19 of the women did believe that sexual discrimination is a problem.Assuming W designates women's responses and M designates men's,which of the following are the appropriate null and alternative hypotheses to test the group's claim?

Instruction 10-5 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 (1) Exam Score After Course (2) 3-3 2 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Instruction 10-5,one must assume that the population of difference scores is normally distributed.

Instruction 10-9 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 10-9,what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions?

Instruction 10-5 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 (1) Exam Score After Course (2) 3-3 2 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Instruction 10-5,the p-value of the test statistic is ________.

A researcher is curious about the effect of sleep on students' test performances.He chooses 60 students and gives each two tests: one given after two hours of sleep and one after eight hours of sleep.The test the researcher should use would be a related samples test.

Given the following information,calculate S_p²,the pooled sample variance that should be used in the pooled-variance t test. S₁² = 4 S₂² = 6 N₁ = 16 n₂ = 25

Instruction 10-4 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: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$ Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$ -Referring to Instruction 10-4,what is the standardised value of the estimate of the mean of the sampling distribution of the difference between sample means?

Instruction 10-4 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: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$ Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$ -Referring to Instruction 10-4,what is the 95% confidence interval estimate for the difference in the two means?

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

The Sydney Morning Herald recently published an article indicating 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 compared to 62% of the women responded "Yes".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.

The F distribution can only have positive values.

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?