Question

We are considering data from the GSS on numbers of close friends people reported having. The mean for this variable is 7.44, with a standard deviation of 10.98. Let's say that you decide to use the GSS data to test whether people who live in rural areas have a different mean number of friends than does the overall GSS sample. Again, treat the overall GSS sample as the entire population of interest. Let's say that you select 40 people living in rural areas and find that they have an average of 3.9 friends.

a. What is the independent variable in this study? Is this variable nominal, ordinal, or scale?

b. What is the dependent variable in this study? Is this variable nominal, ordinal, or scale?

c. What is the null hypothesis for this study?

d. What is the research hypothesis for this study?

e. Would we compare the sample data to a distribution of scores or to a distribution of means? Explain.

Answer 1

a) The independent variable is type of Area. It is nominal variable.

b) Dependent variable is number of close friends people reported having. It is Scale variable.

c) NULL HYPOTHESIS H0:

d) ALTERNATIVE HYPOTHESIS HA:

e) We will compare the sample data to a distribution of means.

Explanation: Here we will compare our sample mean to with population mean and calculate the Z score. If Z score is large enough then we will reject Null Hypothesis H0 at given level of SIGNIFICANCE.

This is the case of Z statisic test.

Z statisic= xbar-mean/sigma/sqrt (n)

Z test = 3.9-7.44/10.98/sqrt (40)