Stat 185 - Problem sheet

Friday, September 18

We’re going to practice another problem in groups today. This should help get you ready for the HW that’s due later today.

You should solve this problems together and then your group should send me one set of solutions as a private message on the forum. I’ll jump around and see how you’re doing.

The problems

  1. According to the American Veterinary Medical Association 38.4% of Americans own dogs. In order to check this to a 90% level of confidence, I surveyed 82 Americans and found that 42 of them owned dogs.
    1. What are p and the corresponding hypothesis test?
    2. What is the standard error?
    3. What are p̂ and its Z-score?
    4. What is the p-value?
    5. What is the conclusion of the test?
  2. In 2018, the national average combined SAT score was 1060. A random sample of 40 UNCA students found an average SAT score of 1158 with a standard deviation of 115. Let’s use this to test the hypothesis that the average UNCA score on the SAT is larger than the national average.
    1. What are μ and the corresponding hypothesis test?
    2. What is the standard error?
    3. What are x̄ and its Z-score?
    4. What is the conclusion of the test?

A comment on sample size: These techniques only work when the sample size is large enough. That’s why problem 3 on the MyOpenMath HW doesn’t work.