Homogeneity example
- 1. Practice Problem Chi-Squared Test for Homogeneity
- 2. Opinion polls used to exclude cell phones from their random digit dialing. If the opinions of people with cell phones differ from those people who have landlines, then the poll may not represent the entire population. A group of people got together and interviewed separate random samples of cell-only and landline telephone users who were less than 30 years old. Do we have sufficient evidence to suggest that the opinion of cell phone users differ from landline users? Cell-Only Sample Landline Sample Democrat 49 47 Independent 15 27 Republican 32 30
- 3. Take a few minutes to work this problem on your own sheet of paper and then flip through this slideshow in order to check your work!
- 4. Hypotheses H0: There is no difference in which type of phone is sampled and the political affiliation for people under 30 years old. Ha: There is a difference in which type of phone is sampled and the political affiliation for people under 30 years old.
- 5. Check conditions: Random – it was stated in the problem that they interviewed separate random samples. Large Sample Size – need to check expected counts to make sure they are all at least 5. EXPECTED COUNTS: Cell-Only Sample Landline Sample Democrat 46.08 49.92 Independent 20.16 21.84 Republican 29.76 32.24
- 6. Do the math! 𝜒2 = (𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑−𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑)2 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝜒2 = (49−46.08)2 46.08 + (47−49.92)2 49.92 + ⋯ (30−32.24)2 32.24 = 3.2199 df: 2 P-value: 0.199897
- 7. State conclusion! Since the p-value is so large, we do not have enough evidence to reject the null hypothesis. There is no difference in which type of phone is sampled and the political affiliation for people under 30 years old.