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.

Step by step solution

01

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$2.$

02

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.

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