91Ó°ÊÓ

Let, the California state university system students took on average $4.5$years with a standard deviation of $0.8$. And the private university students took on average $4.1$years with a standard deviation of $0.3$.

(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 mean time it takes to graduate from a California public institution and a private university.
(d) Normal distribution.
(e) To determine test static as:
To enter the stat list editor, press STAT followed by $1$.

Then ENTER all the values will be:

Hence the test statistics is $2.138$.

(f) The $p$-value from the output is determined as $0.01625$.
(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.

(i) $\mathrm{Î\pm }=0.05$
(ii) Decision: Reject null when $\mathrm{Î\pm }=0.05$; do not reject null when $\mathrm{Î\pm }=0.01$.
(iii) Reason for Decision: $p-$value $<\mathrm{Î\pm }$.
(iv) As a result, there is enough proof to conclude that the mean time it takes to graduate from California state universities is more than that of private universities, at the $5\%$level of significance, .