# Explain the difference between testing a single mean and testing the difference between two means.

1. 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 statistic (z or t). Why is the test appropriate?
h. Find the critical values(s)
i. State the decision
j. Summarize the results.
2. 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 ?
3. 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 â€œbeforeâ€ and â€œafterâ€ test
d. Test scores of a group of students on a math test and a biology test.
4. 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.
5. In a one-way ANOVA, if the test is conducted and the null hypothesis is rejected, what does this indicate?
A. All the population means are equal
B. At least one of the population means are different
C. The normal distribution should be used instead of the F-distribution to determine the critical values of the test
D. None of the above is correct
6. In a one-way ANOVA, there are three treatments with n1 = 5, n2 = 6 and n3 = 5. The rejection region for this test at the 5% level of significance is
A. F > 3.74
B. F > 4.86
C. F > 4.97
D. F > 3.81
7. The following data show samples of three chain stores in three different locations in one town and the amount of dollars spent per customer per visit. At the 0.05 level, is there a difference in among the means?
Store A Store B Store C
30 42 30
14 28 14
22 20 20
18 35 16
26 49 15
25 28
36
24

8. Choose a variable and collect data for at least three different groups (samples). Compare the means of the three groups using the one-way ANOVA technique. Complete the following:
1. Write a brief statement of purpose of the study
2. Define the population
3. State how the sample was selected
4. What a value did you use?
5. State the hypotheses
6. What was F test value?
7. State the decision
8. Summarize the results.