Stat problems for Wednesday, March 17

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. Write down the corresponding hypothesis test as two competing statements $H_0$ and $H_A$. Both should involve an assumed proportion $p$.
   2. What is the standard error?
   3. What are $\hat{p}$ and its $Z$-score?
   4. What is the resulting $p$-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 $\mu$ and the corresponding hypothesis test?
   2. What is the standard error?
   3. What are $\bar{x}$ and its $Z$-score?
   4. What is the conclusion of the test?