A student at a fouryear college claims that mean enrollment

A student at a four-year college claims that mean enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the 35 two–year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Test the hypothesis, assuming a 5% significance level. Solve using the following steps, similar to Appendix-E (Hypothesios Testing with Two Sample Means):

a. State the Null Hypothesis (H_o) and Alternate Hypothesis (H_a)

b. Find the random variable X (remember that X is the difference between the two sample means)

c. State the distribution you will use and why?

d. What is the test statistic (z-score)?

e. What is the critical z?

f. Will you reject or not reject the Null Hypothesis and why?

Solution

A.
Set Up Hypothesis
Null,Ho: u1 = u2
Alternate, mean enrollment at 4-yr colleges is higher than 2-yr colleges H1: u1 < u2

C.

Z Test For Significance of Difference of Means, Since we knows population s.d

D.
Test Statistic
X(Mean)=5068
Standard Deviation(s.d1)=4777
Number(n1)=35
Y(Mean)=5466
Standard Deviation(s.d2)=8191
Number(n2)=35
we use Test Statistic (Z) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=5068-5466/Sqrt((22819729/35)+(67092481/35))
Zo =-0.25
| Zo | =0.25
E.
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo | =0.248 & | Z | =1.645
Make Decision
Hence Value of | Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -0.25 ) = 0.40194
Hence Value of P0.05 < 0.40194,Here We Do not Reject Ho

F.
We don\'t have evidence to indicate that mean enrollment at four–year colleges is higher than at two–year colleges