Question

.In a fishing lodge brochure, the lodge advertises that 75% of its guests catch northern pike over 20

pounds. Suppose that last summer 60 out of a random sample of 87 guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use α = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p = 0.75; H₁: p < 0.75 H₀: p = 0.75; H₁: p ≠ 0.75    H₀: p ≠ 0.75; H₁: p = 0.75 H₀: p < 0.75; H₁: p = 0.75 H₀: p = 0.75; H₁: p > 0.75

(b) What sampling distribution will you use?

The Student’s t, since np > 5 and nq > 5. The Student’s t, since np < 5 and nq < 5.    The standard normal, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value. 

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