Question

Would Not Approve of Driving Drunk	Would Not Care or Would Approve of Driving Drunk
n1=40	n2=25
X¯1=2.1	X¯2=8.2
s1=1.8	s2=1.9

John Worrall and colleagues (2014) found that the fear of losing the good opinion of one’s family and peers kept people from driving home drunk. Let’s say we have two independent random samples of people: those who think that their peers would disapprove of them from driving drunk, and those who think that their peers would either not care or approve of their driving drunk. We ask each person in each group to self-report the number of times that he or she has driven drunk in the past 12 months. The results are in the table above.

Test the null hypothesis that the two population means are equal against the alternative hypothesis that the group whose peers would not approve of driving drunk has a lower mean rate of driving drunk. In your hypothesis test, assume that the unknown population standard deviations are unequal (σ₁ ≠ σ₂), and use an alpha level of .01.

1.Before conducting the appropriate test, first calculate the estimated degrees of freedom, then enter the value you computed in the box. For df, round to three decimal places throughout all calculations, then round your final answer down to the nearest whole integer. (Hint: See this week’s lecture.)

df = ?

2. Now that you have calculated the estimated degrees of freedom, which of the following is the appropriate critical t value for this test? (Hint: Check Appendix table B.3 and remember to round down if necessary for a conservative test.)

A. (±)1.68

B. (±)1.96

C. (±)2.000

D. (±)2.423

E. (±)2.021

3. Conduct the appropriate t test, then enter the value of t_obt you computed in the box. For t_obt, round to 3 decimal places throughout all calculations, then round final value to two decimal places.

t_obt = ?

4. Which of the following statements is the most appropriate conclusion to draw from this test? (Hint: For examples of calculating and interpreting negative t_obt values, see the “Formal Sanction and Intimate Partner Assault” and the “Problem-Oriented Policing and Crime” case studies in Chapter 10 of the book.)

A. Since tobt < tcrit, we have proven the alternative hypothesis. Peer disapproval of drunk driving must be related to one’s own drunk driving behaviors.

B. Since tobt < tcrit, we fail to reject the null hypothesis. There is not enough evidence to reject the assumption that peer disapproval is unrelated to one’s own behaviors.

C. Since tobt > tcrit, we reject the alternative hypothesis. There is enough evidence to conclude that driving drunk leads to peer approval of driving drunk.

D. Since tobt < tcrit, we reject the null hypothesis. It would be highly unlikely to observe a mean difference of this magnitude if the mean rates of driving drunk were truly equal across both groups in the population.

E. Since tobt > tcrit, we fail to reject the alternative hypothesis. The observed difference in sample means is not highly unlikely if the null hypothesis were really true.

Answer 1