A "wild safari" park allows visitors to drive their cars through over 400 acres to see more than 1000 animals roaming freely. The park claims that the probability of some car damage by an animal during a safari drive-thru is 0.65. Suppose 20 cars are selected at random and 18 cars have some damage. Does it appear that the population proportion of cars with some damage exceeds the park's claim?
a. The hypotheses to be tested are H0: p = 0.65 versus Ha: p > 0.65. Clearly define the parameter p in the context of the problem.
b. Report the observed value of the test statistic for testing the hypotheses in part (a).
c. Compute the p-value for this test.
d. If the null hypothesis is true, what is the distribution of the test statistic (that is, which distibution should be used to find the p-value)?
- N(0,1) distribution
- N(0.65, 0.11) distribution
- Bin(n=20, p=0.65) distribution
- Bin(n-20, p=0.90) distribution
e. Our decision at the 5% level of significance is to reject the null hypothesis. Based on our decision, the appropriate conclusion in context is:
- There is not sufficient evidence to conclude that the sample proportion of cars with some damage exceeds the park's claim.
- There is not sufficient evidence to conclude that the population proportion of cars with some damage exceeds the park's claim.
- There is sufficient evidence to conclude that the sample proportion of cars with some damage exceeds the park's claim.
- There is sufficient evidence to conclude that the population proportion of cars with some damage exceeds the park's claim.
f. If the study will be repeated in the future with the same sample size selected from the sample populaton, but now a 10% significance level α will be used, then the probability of correctly rejecting the null hypothesis would:
- increase
- decrease
- stay the same