91Ó°ÊÓ

To conduct a hypothesis test, to determine if the means are statistically the same.

Subscripts : $1=$community college, $2=$four - year university
(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 random variable is the difference between the average text costs and each year's supplies at community institutions, divided by four.
(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 $1.768$.

(f) The $p$-value from the output is determined as $0.0769$.
(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: not reject the null hypothesis.
(iii) Reason for Decision: $p$- value$>\mathrm{Î\pm }$.
(iv) As a result, there is not enough proof to conclude that the mean costs of texts and supplies at community colleges and $4$-year universities is different at the $5\%$level of significance.