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.

Question

Mathematics

Darryl Miranda

17 December, 15:12

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.

+4

Answers (1)

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Bianca Hickman · 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