When students enroll in 4-year colleges, they don't always graduate
on time. In fact, as studies find, the actual time to graduate frequently exceeds four years. A study was conducted to determine if there is a difference in the mean time to graduate for four-year public and private colleges. The table below
shows the summary of the results:
Standard Sample
Mean Deviation Size
Four-year public
institutions
5.6 0.7 81
Four-year private
institutions
5.2 0.4 80
A. Are the assumptions for testing to compare two population means satisfied in this case?
No, the assumptions are not satisfied because at least one sample size is not large enough.
Yes, the assumptions are satisfied because both sample sizes are large enough.
Yes, the assumptions are satisfied since the time to graduate is always normally distributed.
No, the assumptions are not satisfied because the sample sizes are not large enough, and we don't know whether the samples come from normal distribution.
B. State the null and alternative hypothesis. Let 1 public institutions and 2 private institutions.
$H_0: \mu_1 - \mu_2 = 0$, $H_1: \mu_1 - \mu_2 \neq 0$
$H_0: \mu_1 - \mu_2 = 0$, $H_1: \mu_1 - \mu_2 \leq 0$
$H_0: \mu_1 - \mu_2 = 0$, $H_1: \mu_1 - \mu_2 \geq 0$
$H_0: \mu_1 - \mu_2 = 0$, $H_1: \mu_1 - \mu_2 < 0$
$H_0: \mu_1 - \mu_2 = 0$, $H_1: \mu_1 - \mu_2 > 0$
$H_0: \mu_1 - \mu_2 \geq 0$, $H_1: \mu_1 - \mu_2 < 0$
$H_0: \mu_1 - \mu_2 \leq 0$, $H_1: \mu_1 - \mu_2 > 0$
C. What are the test statistic and the P-value?
Test Statistic =
P-value =
Round to 4 decimal places.
Round to 4 decimal places.
D. Are we going to reject or not reject the null hypothesis based on a = 0.05 level of significance?
Because P-value is ?
a=0.05, we ?
the null hypothesis.
E. What is the conclusion of the hypothesis test in the context of the problem?
We have enough evidence to conclude that the average time to graduate is greater for 4-year private institutions as compared to that of public institutions.
We do not have enough evidence to conclude that the average time to graduate is greater for 4-year private institutions as compared to that of public institutions.
We do not have enough evidence to conclude that the average time to graduate is the same for 4-year private institutions as it is for public institutions.
We have enough evidence to conclude that there a significant difference between the time to graduate for 4-year public and private institutions, on average.
We have enough evidence to conclude that the average time to graduate is greater for 4-year public institutions as compared to that of private institutions.
We have enough evidence to conclude that the average time to graduate is the same for 4-year private institutions as it is for public institutions.
We do not have enough evidence to conclude that there a significant difference between the time to graduate for 4-year public and private institutions, on average.
We do not have enough evidence to conclude that the average time to graduate is greater for 4-year public institutions as compared to that of private institutions.
