Answer:
(a) The test statistics that would be used here <u>Two-sample t-test statistics</u> distribution.
(b) The value of t-test statistic is 0.092.
(c) P-value of the test statistics is more than 40%.
Step-by-step explanation:
We are given that of the 35 two-year colleges surveyed, the average enrollment was 5069 with a standard deviation of 4773.
Of the 35 four-year colleges surveyed, the average enrollment was 5216 with a standard deviation of 8141.
Let
= <em><u>average enrollment at four-year colleges in the United States.</u></em>
<u><em /></u>
= <u><em>average enrollment at two-year colleges in the United States.</em></u>
So, Null Hypothesis,
:
{means that the average enrollment at four-year colleges is higher than at two-year colleges in the United States}
Alternate Hypothesis,
:
{means that the average enrollment at four-year colleges is higher than at two-year colleges in the United States}
(a) The test statistics that would be used here <u>Two-sample t-test statistics</u> distribution because we don't know about population standard deviation;
T.S. =
~ ![t__n_1_+_n_2_-_2](https://tex.z-dn.net/?f=t__n_1_%2B_n_2_-_2)
where,
= average enrollment at four-year colleges = 5216
= average enrollment at two-year colleges = 5069
= sample standard deviation at four-year colleges = 8141
= sample standard deviation at two-year colleges = 4773
= sample of four-year colleges surveyed = 35
= sample of two-year colleges surveyed = 35
Also,
=
= 6672.98
So, <em><u>the test statistics</u></em> =
~ ![t_6_8](https://tex.z-dn.net/?f=t_6_8)
= 0.092
(b) The value of t-test statistic is 0.092.
(c) P-value of the test statistics is given by the following formula;
P-value = P(
> 0.092) = More than 40% as this value is not reflected in the t-table.