Answer :
Complete Question
An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.10, he will reject the shipment. He will test the hypotheses
H0: p = 0.10, Ha: p < 0.10.
He selects an SRS of 100 potatoes from the over 2000 potatoes on the truck. Suppose that 6 of the potatoes sampled are found to have major defects. The P-value of this test is.......
Group of answer choices
A 0.4082
B 0.0912
C less than 0.002
D 0.0400
Answer:
Correct option is B
Step-by-step explanation:
From the question we are told that
The null hypothesis is
[tex]H_o: p = 0.10[/tex]
The alternative hypothesis is
[tex]Ha: p < 0.10.[/tex]
The sample size is n = 100
The probability of getting a potatoes that is not defected is [tex]p=0.10[/tex]
The probability of getting a defected potatoes is q = 1-p
The proportion of defected potatoes is mathematically evaluated as
[tex]\r p = \frac{6}{100} = 0.06[/tex]
The test statistics is evaluated as
[tex]t = \frac{\r p - p}{ \sqrt{ \frac{pq}{n} } }[/tex]
substituting values
[tex]t = \frac{0.06 - 0.10}{ \sqrt{ \frac{0.10(1-0.10)}{100} } }[/tex]
[tex]t = -1.333[/tex]
The p-value is 0.0912 from the z-table (you can also use excel formula )