Question

QUESTION 4 A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random 300 peanuts were selected and 21 of them were empty. 1. With a significance level of 1%, can the statement made by the company be accepted? State the null and alternative hypotheses Calculate the critical value Decide 2. With the same sample percentage of empty nuts and 1 - a = 0.95, what sample size would be needed to estimate the proportion of nuts with an error of less than 1%?

Answer 1

Ans:

1)

$H_0:p\leq 0.06$

sample proportion=21/300=0.07

Test statistic:

z=(0.07-0.06)/sqrt(0.06*(1-0.06)/300)

z=0.729

critical z value=2.326

Fail to reject H₀.

2)

sample size required,n=1.96^2*0.07*(1-0.07)/0.01^2

n=2501