Help Please! Find Sample test statistic and P-value

Question

In a fishing lodge brochure, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 71 out of a random sample of 86 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.

Answer 1

n=83

X=71

P estimate =x/n=71/83=0.855

α=0.05

H0=p=0.75

H1=p≠0.75

Zstat=p estimate-p0/√p0(1-p0)/n= 0.105/0.002259=2.209

P value=2*(1-2.209)

=-2.418

α=0.05

We fail to reject null hypothesis and conclude that the data is not statistically significant.

There is insufficient evidence at 0.05 level of significance to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%