Question

A sociologist who studies guns is interested in understanding the differences in gun ownership across the United States, particularly if there is a difference in number of guns owned per household in Majority Republican States (n=18) vs. Majority Democrat States (n=22). 10 states do not have a political lean. (2018 data (Links to an external site.)).

• Sociological note: guns, gun violence, and gun ownership are currently under-studied in the US, particularly because of the lack of funding and data available on this topic. Although we may have some stereotypes about pro-gun attitudes and political affiliation, there isn’t enough research to assume the directionality of the relationship between the majority political opinion of a state and the number of guns owned per household.

Information	Majority Republican States	Majority Democrat States
xbar	1.2 guns	0.5 guns
Standard deviation	0.1	0.2
number in sample	18	22

Answer the following questions. While you are not asked to provide all of the information we have performed on the worksheets in class, following along with the worksheets will help you to answer this problem. Assume that you are performing a t-test at an alpha level of 0.05 (p<0.05).

A) What is the right t-test to use in this case: one-tailed or two-tailed? Why?

B) State your alternative and null hypotheses.

C) What is t-calculated?

D) What is t-critical?

E) Compare t-critical and t-calculated. What decision will you make: reject the null hypothesis, or reject the alternative hypothesis?

F) State your results in a complete sentence as described on the worksheet, including the mathematical portion. Explain what you can (and can’t) determine about the relationship between the variables at hand.

Answer 1

A)

Here, we want to test if there is a difference in number of guns owned per household in Majority Republican States v/s Majority Democrat States. Hence, here we are not intrested to know that which is inferior oe superior. We are only to know if there is any difference or not. So, the two-tailed t-test is best in this case.

B)

C)

Here,

Under , the test statistics is

Where

Now,

D)

  

  

E)

Since |t| calculated is more than t tabulated, So, the null hypothesis may be rejected at 5% level of significance and we may conclude that there is a difference in number of guns owned per household in Majority Republican States v/s Majority Democrat States.