Problem 1

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.

1. The pooled ( i.e. combined ) variance is___________.

1. The computed t statistic is__________.

1. There are _______degrees of freedom for this test.

1. The critical values for a two-tailed test of the null hypothesis of no difference in the population means at the = .05 level of significance are_______.

1. A two-tailed test of the null hypothesis of no difference would______________

( be rejected / not be rejected ) at the = 0.05 level of significance.

Problem 2

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 distribu-tion, the t-test for related samples can be used to determine if there was a significant de-crease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences com-puted as 6.0 pounds.

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1. The t-test should be____________ -tailed.

1. The computed t statistic is__________.

1. There are ________ degrees of freedom for this test.

1. The critical value ( CV ) for a one-tailed test of the null hypothesis of no

difference at the = 0.05 level of significance is _________.

1. A one-tailed test of the null hypothesis of no difference would ________

( be rejected / not be rejected ) at the = 0.05 level of significance.

1. If we were interested in testing against the two-tailed alternative that D

is not equal to zero at the = 0.05 level of significance, the null hypothesis

would___________( be rejected / not be rejected ) .

Problem 3

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.

1. The null and alternative hypotheses that should be tested are__________.

1. The null hypothesis will be rejected if the test statistic ( Z / t ) is ( greater than /

less than ) _____________.

1. The value of the test statistic is__________.

1. The p-value of the test is__________.

1. The null hypothesis should be ( rejected / not rejected )______________.

1. The same decision would be made with this test if the level of significance had

been 0.05 rather than 0.01 ( true / false )_________.