Exam 10: Hypothesis Testing: Two Sample Tests

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

Instruction 10-13 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 10-13,the t test should be ________-tailed.

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 calculated value of the test statistic is ________.

In testing for differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom are

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,suppose ? = 0.05.Which of the following represents the correct conclusion? A)There is no evidence of a difference in the population variances between preservatives A and B. B)There is evidence of a difference in the population variances between preservatives A and B. C)There is evidence that the population variances between preservatives A and B are the same. D)There is no evidence that the population variances between preservatives A and B are the same.

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.For a 0.01 level of significance,what is the critical value for the rejection region?

Instruction 10-11 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 10-11,construct a 95% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

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,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.According to the test run,which of the following is an appropriate alternative hypothesis?

If you are testing for the difference between the means of two independent populations presuming equal variances with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to

Instruction 10-11 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 10-11,the value of the test statistic is ________.

Instruction 10-13 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 10-13,the critical value for a one-tailed test of the null hypothesis of no difference at the α = 0.05 level of significance is ________.

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,what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

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,in testing the difference between two proportions using the normal distribution,you may use a two-tailed Z test.

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

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,what assumptions are necessary for a comparison of the population variances to be valid?

Instruction 10-11 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 10-11,construct a 90% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

Instruction 10-1 Are Chinese managers more motivated than Australian managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL),which measures motivation for upward mobility.The SSATL scores are summarised below. Australian Chinese Sample Size 211 100 Mean SSATL Score 65.75 79.83 Population Std. Dev. 11.07 6.41 -Referring to Instruction 10-1,suppose that the test statistic is Z = 2.45.Find the p-value if we assume that the alternative hypothesis was a two-tailed test (H₁: ?_A - ?_J ? 0).

Instruction 10-1 Are Chinese managers more motivated than Australian managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL),which measures motivation for upward mobility.The SSATL scores are summarised below. Australian Chinese Sample Size 211 100 Mean SSATL Score 65.75 79.83 Population Std. Dev. 11.07 6.41 -Referring to Instruction 10-1,judging from the way the data were collected,which test would likely be most appropriate to employ?

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 10-10,the null hypothesis will be rejected if the test statistic is ________.

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 a point estimate for the mean of the sampling distribution of the difference between the two sample means?