Question

A seatbelt observation study in Massachusetts found that, not surprisingly, male drivers wear
seatbelts less often than women do. The study also noted that men’s belt-wearing jumped more than
16 percentage points when they had a female passenger. Seatbelt use was recorded at 161 locations
in Massachusetts, using random-sampling methods developed by the National Highway Traffic
Safety Administration (NHTSA). Of 4208 male drivers with female passengers, 2777 were belted.
But among 2763 male drivers with male passengers only, 1363 wore seatbelts. Is there a difference
in seatbelt use among male drivers based on the gender of their passenger? Use a significance level
of 5% to test your hypothesis.

a) Define the parameter of interest. Be sure to label the groups your are testing.
b) State the hypotheses statements.
c) Check that the conditions have been and name the significance test to be used.
d) Perform the test and show all work.
e) Interpret the P-value and state your conclusion.
f) Calculate and interpret a 95% confidence interval for the difference in the true proportions.

Answer 1

The solution to this problem is given below