# In what ways is the t distribution similar to the standard normal distribution?

1) In what ways is the t distribution similar to the standard normal distribution? In what ways is the t distribution different from the standard normal distribution? How does the formula for the t test differ from the formula for the z test?

2) Choose a variable. Before collecting the data, decide what a likely average might be, then complete the following:

a. Write a brief statement of purpose of the study

b. Define the population

c. State the hypotheses for the study

d. Select an a value

e. State how the sample was selected

f. Show the raw data

g. Decide which statistical test is appropriate and compute the test

h. statistic (z or t). Why is the test appropriate?

i. Find the critical values(s)

j. State the decision

3) Explain the difference between testing a single mean and testing the difference between two means. What two assumptions must be met when one is using z test to test differences between two means? When can the sample standard deviations s 1 and s 2 be used in place of the population standard deviations s 1 and s 2 ?

4) Explain the difference between independent samples and dependent samples. Classify the following as independent or dependent samples:

a. Weights of identical twins

b. The effectiveness of two different brands of ibuprofen

c. Effect of a new training program on time taken to complete a task, measured by a "before" and "after" test

d. Test scores of a group of students on a math test and a biology test.

5) Complete the following:

a. Select a variable. Compare the mean of the variable for a sample of 30 for one group with the mean of the variable for a sample of 30 for a second group. Use a z test.

b. Select a variable. Compare the mean of the variable for a sample of 10 for one group with the mean of the variable for a sample of 10 for a second group. Use a t test.

c. Select a variable that will enable you to compare proportions of two groups. Use sample sizes of at least 30. Use the z test for proportions

#### Solution Summary

This solution explores basic statistical concepts and contains step-by-step calculations for different tests, distribution types, mean and sample analysis.