Question

Throughout the country, the proportion of first-time, first-year community college students who return for their second year of studies is p = 0.52 according to the Community College Survey of Student Engagement. Suppose a community college institutes new policies geared toward increasing student retention. The first year this policy was in place there were n = 2843 first-time, first-year students (N = 1, 050,000). Of these students, x = 1516 returned for their second year of studies. Treat these students as a random sample of all first-time, first year students. ?̂ = 0.533. Conduct the appropriate hypothesis test to determine if a higher proportion of community college students returned for their second year, after the new student retention policy. Use α = 0.05
a. Step 1: Verify the assumptions for the Distribution of the Sample Proportion ?̂ (3 pts)
• Sample is random
• Distribution is normally distributed, if n?0(1- ?0) ≥ 10
• n ≤ 0.05 of N
b. Step 2: State the null and alternative hypotheses (1 pt.):
c. Step 3: Determine the level of significance, α (1 pt.):
d. Step 4a: Calculate the test statistic (2 pts):
?0= ? ̂ − ?0√?0(1−?0)?
e. Step 4b: Determine the p-value of the test statistic (1 pt.):
f. Step 5: Compare the p-value of the test statistic to the alpha level, and decide whether to reject or retain Ho (1 pt.):
g. Step 6: State the conclusion of the hypothesis test in a full sentence (1 pt.):

Answer 1