## 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**

- P = 1 – P(Z<1.11) = 1 – 0.8665 =
**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.

- A nationwide survey reports
- 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. *