# T-tests and z-tests

How many variables are in a Z and T test? What are they? What are their levels of measurement?

What is the underlying difference between the T-test and the Z-test?

Provide an example of nominal information and write a work related survey question that would collect nominal data:

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#### Solution Preview

A.

A z test is typically used to compare a single sample to a population on a single variable. For example, you could use a z test to test whether a group of people are overweight relative to the rest of the population. A z test can also be used to determine whether a single individual's score is typical in a population. For example, if you took an IQ test, your performance on the test may be described in terms of a z score. Again, this would be done for a single variable (IQ). Z tests can handle a variety of different variables, but they must be measured on a continuous, interval or ratio scale of measurement.

A t test can be used to compare the following: a single sample to a population, two samples, or paired scores (for example, if you wanted to compare pre- ...

#### Solution Summary

Explains z and t tests and their underlying differences. Also gives an example of a survey question that would collect nominal data.

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