Question

A publisher reports that 22% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually above the reported percentage. A random sample of 250 found that 29% of the readers owned a personal computer. Is there sufficient evidence at the 0.01 level to support the executive's claim?

Step 1 of 6:

State the null and alternative hypotheses.

Step 2 of 6:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6:

Specify if the test is one-tailed or two-tailed.

Step 4 of 6:

Determine the decision rule for rejecting the null hypothesis, H0

Step 5 of 6:

Make the decision to reject or fail to reject the null hypothesis.

Step 6 of 6:

State the conclusion of the hypothesis test.

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.22
Alternative Hypothesis, Ha: p > 0.22

2)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.29 - 0.22)/sqrt(0.22*(1-0.22)/250)
z = 2.67

3)

the test is one-tailed

4)

decision rule:
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

4)

reject the null hypothesis.

6)

THere is sufficient evidence to test the claim that the percentage is actually above the reported percentage