\"The phenomenon of road rage has been frequently discussed but infrequently exa

Question

"The phenomenon of road rage has been frequently discussed but infrequently examined." So begins a report based on interviews with 1382 randomly selected drivers. The respondents' answers to interview questions produced scores on an "angry/threatening driving scale" with values between 0 and 19. Does the driver's age affect road rage? Here are the mean responses for three age-groups.

The report says that F = 34.96 with p-value < 0.01.

(a) What is the null hypothesis for the ANOVA F test?

All age groups have the same mean response.

All age groups have a different mean response.    

At least one age group has a different mean response.

(b) What is the alternative hypothesis for the ANOVA F test?

All age groups have the same mean response.

All age groups have a different mean response.    

At least one age group has a different mean response.

(c) Based on the sample means and the results of the ANOVA, what do you conclude at the = 0.05 level?

There is sufficient evidence at the = 0.05 level that all of the age groups have the same mean "road rage" score.

There is sufficient evidence at the = 0.05 level that the at least one of the age groups has a different mean "road rage" score.    

There is insufficient evidence at the = 0.05 level that all of the age groups have the same mean "road rage" score.

There is insufficient evidence at the = 0.05 level that the at least one of the age groups has a different mean "road rage" score.

Explanation / Answer

1. Null hypothesis:

All age groups have the same mean response.

2. Alternate hypothesis:

At least one age group has a different mean response.

3. Interpretation of F=34.96 and p-value < 0.01 at 0.05 level:

p-value is the key metric to be considered in ANOVA test, and if p-value is lesser than the significance level, reject the null hypothesis and conclude that not all of population means are equal. Hence the right option is:

There is sufficient evidence at the = 0.05 level that the at least one of the age groups has a different mean "road rage" score.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.