Exam 10: Hypothesis Testing: Two-Sample Tests

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,construct a 90% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

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,construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

Instruction 10-6 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 10-6,the p-value for a two-tailed test whose computed t statistic is 2.50 is between __________ and __________.

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,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?

Instruction 10-6 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 10-6,what is the 95% confidence interval estimate for the difference in the two means?

Instruction 10-10 A few years ago, Pepsi invited consumers to take the "Pepsi Challenge". Consumers were asked to decide which of the two soft drinks, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Males: n = 109, $p _ { M }$ = 0.422018 Females: n = 52, $p _ { F }$ = 0.25 $p _ { M }$ - $p _ { F }$ = 0.172018 Z = 2.11825 -Referring to Instruction 10-10,construct a 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

For a two-tail test with a given level of significance $\alpha$ ,you reject the null hypothesis if the calculated t test statistic is less than the upper-tail critical value tn-1 from the t distribution.

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 should be rejected.

Instruction 10-5 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Material Primary Supplier Secondary Difference Supplier 1 \ 55 \ 45 \ 10 2 \ 48 \ 47 \ 1 3 \ 31 \ 32 -\ 1 4 \ 83 \ 77 \ 6 5 \ 37 \ 37 \ 0 6 \ 55 \ 54 \ 1 Sum: \ 309 \ 292 \ 17 Sum of Squares: \ 17,573 \ 15,472 \ 139 -Referring to Instruction 10-5,the hypotheses that the buyer should test are a null hypothesis that _______ versus an alternative hypothesis that __________.

Instruction 10-10 A few years ago, Pepsi invited consumers to take the "Pepsi Challenge". Consumers were asked to decide which of the two soft drinks, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Males: n = 109, $p _ { M }$ = 0.422018 Females: n = 52, $p _ { F }$ = 0.25 $p _ { M }$ - $p _ { F }$ = 0.172018 Z = 2.11825 -Referring to Instruction 10-10,suppose Pepsi wanted to test to determine if the males preferred Pepsi more than the females.Using the test statistic given,compute the appropriate p-value for the test.

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,what is the 95% confidence interval estimate for the difference in the two means?

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 same decision would be made if this had been a two-tailed test at a level of significance of 0.01.

Instruction 10-5 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Material Primary Supplier Secondary Difference Supplier 1 \ 55 \ 45 \ 10 2 \ 48 \ 47 \ 1 3 \ 31 \ 32 -\ 1 4 \ 83 \ 77 \ 6 5 \ 37 \ 37 \ 0 6 \ 55 \ 54 \ 1 Sum: \ 309 \ 292 \ 17 Sum of Squares: \ 17,573 \ 15,472 \ 139 -Referring to Instruction 10-5,the decision rule is to reject the null hypothesis if__________.

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 10-14 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 same decision would be made with this test if the level of significance had been 0.05 rather than 0.01.

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

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,the value of the sample mean difference is __________ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

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,suppose $\alpha$ = 0.01.Which of the following represents the result of the relevant hypothesis test?

The F test used for testing the difference in two population variances is always a one-tailed test.

Instruction 10-5 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Material Primary Supplier Secondary Difference Supplier 1 \ 55 \ 45 \ 10 2 \ 48 \ 47 \ 1 3 \ 31 \ 32 -\ 1 4 \ 83 \ 77 \ 6 5 \ 37 \ 37 \ 0 6 \ 55 \ 54 \ 1 Sum: \ 309 \ 292 \ 17 Sum of Squares: \ 17,573 \ 15,472 \ 139 -Referring to Instruction 10-5,what is the 95% confidence interval estimate for the mean difference in prices?