Question

A buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten. Unless there is clear evidence that this proportion is less than 0.06, she will reject the shipment. To reach a decision she will test the hypotheses

 ,  . To do so, she selects an SRS of fifty apples from the over 20000 apples on the truck.



Suppose that only two of the apples sampled are found to have major defects, and she proceeds with the test. The P-value of her test is

Answer 1

P value = 0.23527 which is greater than 0.10

Explanation:

Given :

Phat = proportion of rotten apple = 2/50 = 0.04

1 - phat = 0.96

p = 0.06

Tstatistic = (Phat - p) / sqrt[(Phat(1-Phat))/n]

Tstatistic = (0.04 - 0.06)/sqrt[(0.04(0.96))/50]

Tstatistic = (-0.02) / 0.0277128

Tstatistic = - 0.7216

Pvalue of Tstatistic

P(Z < - 0.7216) = 0.23527 (Pvalue calculator)