Question

A publisher reports that 23% 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 300 found that 29% of the readers owned a personal computer. Is there sufficient evidence at the 0.10 level to support the executive's claim?

Step 1 of 7:

State the null and alternative hypotheses.

Step 2 of 7:

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

Step 3 of 7:

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

Step 4 of 7:

Determine the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 7:

Identify the value of the level of significance.

Step 6 of 7:

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

Step 7 of 7:

State the conclusion of the hypothesis test.

Answer 1

Solution :

Given that,

= 0.23

1 - = 0.77

n = 300

Level of significance = = 0.10

Point estimate = sample proportion = = 0.29

Step 1 of 7:

The null and alternative hypothesis is,

Ho: p = 0.23

Ha: p 0.23

Step 2 of 7:

This a right (One) tailed test.

Step 3 of 7:

Test statistics

z = ( - ) / *(1-) / n

= ( 0.29 - 0.23) / (0.23*0.77) / 300

= 2.4690

Step 4 of 7:

Critical value of  the significance level is α = 0.10, and the critical value for a right-tailed test is

= 1.28

Step 5 of 7:

Since it is observed that z = 2.4690 > = 1.28, it is then concluded that the null hypothesis is rejected.

Step 6 of 7:

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the percentage is actually above the reported percentage. at the α = 0.10 significance level.