Question

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of $60$high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be $6$hours with a standard deviation of $3$hours. The researcher also obtained an independent SRS of $40$high school students in a large city school district and found the mean time spent in extracurricular activities per week to be $5$hours with a standard deviation of $2$hours. Suppose that the researcher decides to carry out a significance test of ${\mathrm{H}}_0$: μsuburban=μcity versus a two-sided alternativ

The P-value for the test is $0.048$. A correct conclusion is to

a. fail to reject ${\mathrm{H}}_0$because$0.048<\alpha =0.05$. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

b. fail to reject ${\mathrm{H}}_0$because $0.048<\alpha =0.05$. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

c. fail to reject ${\mathrm{H}}_0$because$0.048<\alpha =0.05$. There is convincing evidence that the average time spent on extracurricular activities by students in the suburban and city school districts is the same.

d. reject ${\mathrm{H}}_0$because $0.048<\alpha =0.05$. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

e. reject ${\mathrm{H}}_0$because $0.048<\alpha =0.05$ . There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

Short answer

Option (e) reject ${\mathrm{H}}_0$because $0.048<\alpha =0.05$. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts is the correct conclusion.

Step-by-step solution

Given information

We need to find correct conclusion.

Simplify

As we know,

The following is the p-value for the test:
$P=0.048$
As we all know, the null hypothesis is rejected if the P-value is less than or equal to the significance level:
$P<0.05\to$Reject $\alpha$
There is enough data to suggest that the population means differ.
As a result, the proper choice is (e), which is to reject $H_0$because $0.48<\alpha =0.05$
There is compelling evidence that children in suburban and city school districts spend different amounts of time on extracurricular activities.