1. Given the above information, what kind of hypothesis test will you conduct? Should it be α-test, z-test, t-test, χ2-test, F-test, or Ω-test? Please explain.
2. What will be the null hypothesis, the alternative hypothesis, and, hence, the "tailedness" of the test (left-tailed, right-tailed, or two-tailed)?
3. What is be the corresponding test statistics?
4. What is the corresponding p-value of the hypothesis test?
5. What kind of conclusion can you draw from the hypothesis test you have just performed? Of course, representatives of ntbnP would like to have the conclusion skewed to their advantage. And so would the officials from FDA. What would you do if you are representing ntbnP? But, if you are representing FDA, how would you present your argument?
We can see that the p-value for the test is small. Considering a significance level of 0.05 we are rejecting the null hypothesis as p-value is smaller than the significance level. Thus the data gives sufficient evidence that the claim of ntbnP is false.
6. But, wait. What if FDA actually does not know the population standard deviation in this case, would you conduct your hypothesis test different? Just in case that you are going to perform the hypothesis different, what would you do instead?
7. My brother wants to estimate the proportion of Canadians who own their house. What sample size should be obtained if he wants the estimate to be within 0.02 with 90% confidence if
a. he uses an estimate of 0.675 from the Canadian Census Bureau?
b. he does not use any prior estimates? But in solving this problem, you are actually using a form of "prior" estimate in the formula used. In this case, what is your "actual" prior estimate? Please explain.
8. An amusement park is considering the construction of an artificial cave to attract visitors. The proposed cave can only accommodate 36 visitors at one time. In order to give everyone a realistic feeling of the cave experience, the entire length of the cave would be chosen such that guests can barely stand upright for 98% of the all the visitors.
The mean height of American men is 70 inches with a standard deviation of 2.5 inches. An amusement park consultant proposed a height of the cave based on the 36-guest-at-a-time capacity. Construction will commence very soon.
The park CEO has a second thought at the last minute, and asks yours truly if the proposed height is appropriate. What would be the proposed height of the amusement park consultant? And do you think that it is a good recommendation? If not, what should be the appropriate height? Why?