Lizzy and Arthur were arguing over a news feed about a population of catfish that had figured

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Question:

Lizzy and Arthur were arguing over a news feed about a population of catfish that had figured out how to hunt feral pigeons. A submerged catfish lying in wait would rush into shallow water (like a killer whale beaching itself when hunting seals), grab a pigeon that had been drinking or bathing at the water’s edge, drag it into deeper water, and swallow it. Lizzy was skeptical and suggested that if the story had merit, the chance of a successful capture would surely be low: 20% or less. Arthur suspected that for the strategy to be profitable, the success rate would need to be fairly high, perhaps as high as 40%. To investigate, they tracked down the original data, which reported that 18 out of 64 attempts were successful.

(a) Refer to catfish problem description. Recall that the original data reported that 18 out of 64 attempts were successful. Assume that this was a random sample and it seems reasonable to use the normal approximation. Obtain a 93% confidence interval and fill-in the blanks:

We are 93% confident that the percentage of successful attempts is between (lower bound)--------- and (upper bound) -----------.

(b) Based on the results obtained, are these data consistent with Lizzy's conjecture? Yes or No

(d) Refer to catfish problem description. Perform a test of significance to test Lizzy's claim that the percentage of successful attempts is 20% (0.2) or less and determine if there is evidence that it is actually greater than 20%. What is the test statistic?

(e) Refer to catfish problem description. Perform a test of significance to test Lizzy's claim that the percentage of successful attempts is 20% or less and determine if there is evidence that it is actually greater than 20%. Based on the test statistic obtained for this test of significance, what is the p-value?

(f) Refer to catfish problem description. After performing a test of significance to test Lizzy's conjecture that the percentage of successful attempts is 20% or less and using a significance level equal to 0.05, you (1) "reject",or (2) "fail to reject", " (3) are unsure whether or not to reject" the null hypothesis; that is, (1) "you have found", (2) "you haven't found", (3) "the results obtained, perhaps, represent marginal" evidence to support the conclusion that the percentage of successful attempts is actually greater than 20%.