Question

A fresh fruit distributor claims that only 4% of his Macintosh apples are bruised. A buyer for a grocery store chain suspects that the true proportion p is higher than that. She takes a random sample of 30 apples to test the null hypothesis H0: p = 0.04 against the alternative hypothesis Ha: p > 0.04. Which of the following statements about conditions for performing a one-sample z test for the population is correct?
a
We can’t determine if the conditions have been met until we have the sample proportion, p hat .
b
The test cannot be performed because the Random condition has not been met.
c
All conditions for performing the test have been met.
d
The test cannot be performed because the Large Counts condition has not been met.

Answer 1

Answer: For the answer to the question above, 

P-value is determined by finding the z-value for the sample: 

z = (17 - 20) / [6 / sqrt(9)] = -1.5 

Look up in a Normal table P(z < - 1.5) = 0.0668. But, multiply this times 2 since this is a two-tailed test (μ≠ 20): 

P-value = 0.0668(2) = 0.1336