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 $H_{0:}{\mu }_{\text{mibratum}}={\mu }_{\text{cilly}}$versus a two-sided alternative

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

(a) fail to reject $H_0$at the role="math" localid="1650370033639" $\alpha =0.05$level. 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 $H_0$at the role="math" localid="1650370045107" $\alpha =0.05$level. There is no 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 $H_0$at the role="math" localid="1650370055451" $\alpha =0.05$level. 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 $H_0$at the role="math" localid="1650370062817" $\alpha =0.05$level. There is no convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

(e) reject $H_0$ at the role="math" localid="1650370172076" $\sigma =0.05$ level. 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

The correct conclusion is option (e) reject $H_0$at the$\alpha =0.05$ level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

Step-by-step solution

Given information

The first number of high school is$60$

Mean is$6$

Standard deviation is$3$

The second number of high school is$40$

Mean is$5$

Standard deviation is$2.$

Explanation

The given value is

$P=0.048$

The null hypothesis is rejected if the $P$-value is less than or equal to the significance level:

$P<0.05\Rightarrow Reject{H}_0$

There is sufficient evidence of a difference between the population means reject $H_0$ at the $\alpha =0.05$level.