Chapter 10: Q. T10.6 (page 698)

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 $H_{0}$ : 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 $H_{0}$ because $0.048 < α = 0.05$ . 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 $H_{0}$ because $0.048 < α = 0.05$ . 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 $H_{0}$ because $0.048 < α = 0.05$ . 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 $H_{0}$ because $0.048 < α = 0.05$ . 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 $H_{0}$ because $0.048 < α = 0.05$ . 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

Expert verified

Option (e) reject $H_{0}$ because $0.048 < α = 0.05$ . 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 $α$
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 $0.48 < α = 0.05$
There is compelling evidence that children in suburban and city school districts spend different amounts of time on extracurricular activities.