Guest Lecture: Hypothesis Testing for Proportions

April 17, 2017

Mon, Apr 17

• Hypothesis Testing with Proportions:
  • Test statistics for proportions are different.
  • Instead of Z = (x̅ – μ)/(σ/√n) we use Z = (p̂- po)/ [√(p̂)*(1 – p̂)/n] for proportions.
  • Aside from the test statistic, we use the same procedure.

• Example C: Are CSU-Pueblo students more likely to have a job outside of school?
  • A nationwide survey reports 72% of undergraduate college students work while enrolled in school.
  • You want to test whether this percent is different at CSU-Pueblo so you randomly sample 100 students and 77 say they are currently working.
  • Step 1: Setup the hypothesis test
    • Ho: p = 0.72
    • Ha: p > 0.72
    • p̂ = 77/100 = 0.77
    • n = 100
  • Step 2: Calculate the appropriate test statistic
    • Z-test = (p̂- po)/ [√(p̂)*(1 – p̂)/n]
    • (0.77 – 0.72)/[√(0.72)*(1 – 0.72)/100] = 0.05/0.045 = 1.11
  • Step 3: Find P-value
    • P = 1 – P(Z<1.11) = 1 – 0.8665 = 0.1335
  • Step 4: Interpret results
    • 0.1335 ≅ 13.35% probability of getting result by chance
    • 0.1335 > 0.05
    • Fail to Reject Ho
    • Not sufficient evidence to claim more CSU-Pueblo students work than national average.
• Inference for Proportions (10:46)

Activity:

• Problem 2.1. A large national survey of workers from a variety of occupations reported 25% of workers said work stress had a negative impact on their personal lives. In a separate survey of n = 100 restaurant workers, 32 indicated work stress had a negative impact on their personal lives. Is there evidence to suggest restaurant workers deal with more stress than average?

* Most example and activity problems presented are derived from Moore, D.S., McCabe, G.P., and Craig, B.A., 2009. Introduction to the Practice of Statistics, 6th Edition. New York: W.H. Freeman and Company.