Question

In a study that followed a group of students who graduated from high school in 1997, each was monitored in progress made toward earning a bachelor’s degree. The group was divided into two – those who started at community college and later transferred to a four-year college (group 1), and those that started out in a four-year college as freshmen (group 2). The data below summarize the findings:

	Community College Transfers	Non-Transfers
n	317	1,297
Mean Time to Graduate	5.12	4.75
Population Standard Dev. Time to Graduate (in years)	1.996	1.075

Is there evidence to suggest that community college transfer students take longer to earn a bachelor’s degree? Use α=0.05.

Select the correct alternative hypothesis and the p-value.

• A.

  H1: µ1 ≠ µ2;   p-value = 0.0007

• B.

  H1: µ1 > µ2;   p-value = 0.0007

• C.

  H1: µ1 < µ2; p-value = 0.0007

• D.

  H1: µ1 ≠ µ2; p-value = 0.001426

• E.

  H1: µ1 > µ2; p-value = 0.001426

• F.

  H1: µ1 < µ2;   p-value = 0.001426

Answer 1

Solution: Community College Transfer: ni = 317 01 = 1.996 ži = 5.12 No Transfer: n2 = 1297 02 = 1.075 2 = 4.75 Null Hypothesis: Ho: M1 = 42 Alternative Hypothesis: HA: M1 > H2 Test Statistic: [(x1 - x2) - (U1 – U2)] Z= + o? _ož ni N2 [5.12 – 4.75 – (0)] Z= 1.9962 1.0752 + 317 1297 z= 3.19 P-value: From normal distribution table, the area in the upper tail to the right of (z = 3.19), is given by = 0.0007 Hence, p-value = 0.0007 a = 0.05 Since p-value <a, we reject the null hypothesis Ho. Reject the null hypothesis. The evidence does suggest that community college transfer students take longer to attain a bachelor's degree at the a=0.05 level of significance.