Question

A driver's ed program is curious if the time of year has an impact on the number of car accidents in the U.S. They assume that weather may have a significant impact on the ability of drivers to control their vehicles. They take a random sample of 150 car accidents and record the season each occurred in. They found that 27 occurred in the spring, 39 in the summer, 31 in the fall, and 53 in the winter. Can it be concluded at the 0.05 level of significance that car accidents are not equally distributed throughout the year?

Hypotheses:

H0: Car accidents are equally distributed throughout the year.
H1: Car accidents are not equally distributed throughout the year.
Select the best fit choices that fit in the two blank spaces above.

a) Are, Are not

b) Are not, Are

c) Are, Are

d) Are not, Are not

Answer 1

Option B: The correct choices for the blank spaces are 'Are not', 'Are'. We can use a chi-square test with a significance level of 0.05 to determine if car accidents are equally distributed throughout the year.

Step-by-step explanation:

If the p-value is less than 0.05, we reject the null hypothesis.

The correct choices to fill in the two blank spaces are Are not, Are.

Null hypothesis (H0): Car accidents are equally distributed throughout the year.

Alternative hypothesis (H1): Car accidents are not equally distributed throughout the year.

To determine if car accidents are equally distributed throughout the year, the chi-square test can be used. In this case, we have four seasons (spring, summer, fall, and winter) and the observed frequencies are 27, 39, 31, and 53, respectively.

Using a chi-square test with 3 degrees of freedom and a significance level of 0.05, we compare the expected frequencies with the observed frequencies.

Based on the chi-square test statistic and its associated p-value, if the p-value is less than 0.05, we reject the null hypothesis and conclude that car accidents are not equally distributed throughout the year.