A luxury housing developer is evaluating several local lakes they hope to develop a housing community at the lake that has the most abundant source of fish for potential tenants The developer found that 18 of the 34 fishing trips they had their employees go on resulted in fish being caught.

A) suppose the lake Wayne authority claims that "only at this lake will you catch fish on at least 67% of your trips". A statistician to evaluate the authories' claim using a hypothesis test. Describe the meaning of a Type 1 and Type 2 error in this situation. Which do you think would be worse for the housing developer? Note: don't actually do a hypothesis test

B) Assuming that the fishing trips taken by the employees constitute a random sample, construct a 95% confidence interval for the true proportion of trips resulting in a fish being caught.

C) Based on your interval in part B, is the lake authorities claim reasonable? why or why not?

D) The other lake the developer is currently evaluation is Lake Britt. The land at Lake Britt is cheaper, so the developer would prefer it over Lake Wayne if there is no difference in the percentage of successful fishing trips. Suppose a random sample of 42 fishing trips found that 13 were successful. Using alpha = 0.05, test whether the true proportion of successful fishing trips at Lake Britt differs from Lake Wayne.