Exam 10: Hypothesis Testing: Two-Sample Tests

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,a two-tailed test of the null hypothesis of no difference would__________ (be rejected/not be rejecteat the $\alpha$ = 0.05 level of significance.

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,if the buyer had decided to perform a two-tailed test,the p-value would have been between __________ and __________.

Observations that are analysed together on the basis of a common characteristic are known as paired observations.

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).

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

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,to determine if a difference exists in the taste preferences of men and women,give the correct alternative hypothesis that Pepsi would test.

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,if the firm wanted to test whether a greater proportion of workers would currently like to attend a self-improvement course than in the past,which represents the relevant hypotheses?

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,in examining the differences between related samples you are essentially sampling from an underlying population of difference "scores".

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

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 10-10 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 same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

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 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

Instruction 10-9 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. Preservative A Preservative B =106.4 =56.54 =10.3 =13.4 -Referring to Instruction 10-9,state the null and alternative hypotheses for testing if the population variances differ for preservatives A and B

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 p-value for a one-tailed test whose computed t statistic is 2.00 is between __________and __________.

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 99% confidence interval estimate for the mean difference in prices?