91Ó°ÊÓ

To determine the mean cost for auto insurance for teenage boys is greater than that for teenage girls. Then to conduct a hypothesis test to evaluate the manufacturers claim.

Subscripts : $1=$boys, $2=$girls
(a) The null hypothesis is described as follows:
$H_0:{\mathrm{μ}}_1≤{\mathrm{μ}}_2$
(b) The alternate hypothesis is described as follows:
$H_a:{\mathrm{μ}}_1>{\mathrm{μ}}_2$
(c) The difference in the mean auto insurance costs for boys and girls is the random variable.
(d) Normal distribution.
(e) To determine the test static as:
To access the stat list editor, click STAT and then 1.

Then ENTER all the values the OUTPUT will be:

Hence, the test statistics is $2.497$.

(f) The $p$-value from the output is determined as $0.00625$.
(g) Obtain a clear picture of the situation using the information from the last task.
The horizontal axis should be named and measured, and the region(s) on the graph that correlate to the $p$-value should be shaded.

(h)

(i) $\mathrm{Î\pm }=0.05$
(ii) Decision: reject the null hypothesis.
(iii) Reason for Decision: $p-$value $<\mathrm{Î\pm }$.
(iv) As a result, there is enough proof to conclude that the mean cost of auto insurance for teenage boys is more than that for girls, at the $5\%$level of significance.