Question

3. A quality control inspector claims that over 10% of microwaves need repairs during the first five years of use. A researcher is testing this claim.

a. Write the null and alternative hypotheses, and tell whether the test is left-tailed, right-tailed, or two-tailed.

b. In a random sample of 114 microwaves, 16 needed repairs during the first five years. Find the test statistic.

c. Find the P-value.

d. The level of significance for this hypothesis test is 0.05. Should the researcher reject the null hypothesis or fail to reject the null hypothesis?

e. Write a conclusion in the context of the quality control inspector’s claim about microwaves.

Answer 1

a)

H0: p = 0.10

Ha: p > 0.10

This is right tailed test.

b)

Sample proportion = 16 / 114 = 0.1404

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.1404 - 0.10) / sqrt [ 0.10 ( 1 - 0.10) / 114 ]

= 1.44

c)

p-value = P(Z > z)

= P(Z > 1.44)

= 0.0749

d)

Since p-value > 0.05 , Reject the null hypothesis.

e)

We do not have sufficient evidence to conclude that over 10% of microwaves need repairs

during the first five years of use.