Help on number 2

Question

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 four-year colleges surveyed, the mean enrollment was 5,197 with a standard deviation of 559. Of the 35 two-year colleges surveyed, the mean enrollment was 4,580 with a standard deviation of 499. Test the student's claim at the 0.01 significance level.

Preliminary:

1. Is it safe to assume that
2.  of all students enrolled at a 4-year college in the Unites States and
3.  of all enrolled at a 2-year college in the Unites States?
4. Yes
5. No
6. Is N4yr >_ 30 and N2yr >_30 ?
7. No
8. Yes

Test the claim:

1. Determine the null and alternative hypotheses. 
2. Ho: ? > ≠ < =   
3. Ha: ? > = < ≠   
4. Determine the test statistic. Round to four decimal places. T=
5. Find the p-value. Round to 4 decimals.
6. P-value = 
7. Make a decision. 
8. Fail to reject the null hypothesis.
9. Reject the null hypothesis.
10. Write the conclusion. 
11. There is sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.
12. There is not sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.

Answer 1

Hi Morgan,

Preliminary

#1-3. I can't understand those questions. It is not clear what they are asking you for.

#4. Yes. You have 35 of each type of college, which exceeds 30.

Test the Claim:

#1. If you are discussing averages, H0 involves mu, so if we call the four-year college mean enrollment mu1 and the two-year mu2:

H0: mu1 = mu2

Now, you want to know if 4-year mean enrollment exceeds 2-year, so:

Ha: mu1 > mu2

#4. Two ways to do this—first way is to use a TI-80s series calculator. Go to STAT-TESTS-2SampTTest--enter xbar1(5197), s1 (559), n1 (35), xbar2 (4580), s2 (499), n2 (35). change alternative to mu1 > mu2, Pool: no; calculate. You will get t-test statistic, p-value, sample means and standard deviations, and degrees of freedom.

Second way is longer, but you may have to use it if you do not have a TI-80s series calculator.

Formula is:

T = (xbar1 -xbar2) - 0 / sqrt[s1²/n1) + (s2²/n2)]

Xbar1= Sample 1 Mean = 5197

Xbar2= Sample 2 Mean = 4580

S1= Sample 1 standard deviation = 559

S2= Sample 2 standard deviation = 499

N1= Sample 1 Size = 35

N2= Sample 2 Size = 35

#6. P-value can be found in calculator as described above or from statistical software. You can also get it from a t-table but this is less precise—you can only get a range, not an actual p-value that you can round to 4 decimals.

#7 and 8. This depends on your p-value. Your problem gives significance level alpha as 0.01, so I’ll go with it here. If your p-value falls below 0.01, reject H0. If it exceeds 0.01, fail to reject H0. If you reject, there is sufficient evidence that mean enrollment is higher in four-year colleges than two-year colleges. If you fail to reject, there is not sufficient evidence that mean enrollment is higher at four-year colleges than two-year colleges.

I hope this helps.