# Z tests & t tests

1. If two independent samples are used in a hypothesis test concerning the difference between population means for which the combined degrees of freedom is 20, which of the following could not be true about the sample sizes n1 and n2?

A) n1=12 and n2=8

B) n1=12 and n2=10

C) n1=13 and n2=9

D) Cannot be determined from the given information

2. To test the null hypothesis that the mean waist size for males under 40 years equals 34 inches versus the hypothesis that the mean differs from 34, the following data were collected: 33, 33, 30,

34, 34, 40, 35, 35, 32, 38, 34, 32, 35, 32, 32, 34, 36, 30.

Calculate the t* -value of the test statistic.

3. State the null hypothesis, Ho,and the alternative hypothesis, Ha , that would be used to test the claim: The standard deviation has increased from its previous value of 15.

4. A particular candidate claims she has the support of at least 60% of the voters in her district. A random sample of 150 voters yields 87 who support her. The candidate wishes to test her claim at the 0.05 level of significance.

Compute the value of test statistic.

5. A random sample of 51 observations was selected from a normally distributed population. The sample mean was x = 88.6 , and the sample variance was s2 = 38.2. We wish to determine if there is sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance.

Calculate the value of the test statistic.

6. Consider testing Ho: μd ≤ 0 vs. Ha: μd = > 0 with n =20 and t∗ =1.95.

Place bounds on the p-value using the table of "critical values of Student's t-distribution" available in your textbook.

7.

Consider the following paired data.

A 5 4 3 4 1

B 2 1 5 4 3

Calculate Σd , Σd 2 , d(bar), and sd .

8. A group of sheep, infested with tapeworms, are randomly divided into two groups as follows. Each sheep is assigned a number (1 through 20) and then 10 numbers are selected by drawing 10 slips of paper from a box having the numbers 1 through 20 written on them. The drawing divides the sheep into two groups. One group is given a placebo and the other is given an experimental drug. After six weeks the sheep are sacrificed and tapeworm counts are made. Do these samples represent dependent or independent samples?

9. You plan to test the dependent sampling claim: "a particular weight loss program is effective in weight reduction." What would be the null hypothesis, if d=X after −X before?

A) Ho: μd = 0

B) Ho: μd = 0 (≥)

C) Ho: μd ≠ 0

D) Ho: μd = 0 (≤)

10. If two independent samples are used in a hypothesis test concerning the difference between population means for which the combined degrees of freedom is 20, which of the following could not be true about the sample sizes n1 and n2?

A) n1=12 and n2=8

B) n1=12 and n2=10

C) n1=13 and n2=9

D) Cannot be determined from the given information

#### Solution Summary

The solution examines z tests and t tests for null hypothesis. The value of the test statistic is determined.