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. If there is clear evidence that this proportion is less than 0.10, she will accept the shipment. To reach a decision, she will test the hypotheses H0: p = 0.10 vs. H a: p < 0.10. To do so, she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck. Only 8 of the potatoes sampled are found to have major defects. The large sample z statistic is calculated to be z = −1.91. What is the P-value for this hypothesis test?

• A. Less than 0.0002
• B. 0.0098
• C. 0.0281
• D. 0.0568

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p =0.10

Ha : p < 0.10

z= -1.91

P(z <-1.91 ) = 0.0281 using z table

P-value = 0.0281