Question

A publisher reports that 39% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually more than the reported percentage. A random sample of 250 found that 48% of the readers owned a laptop. Is there sufficient evidence at the 0.02 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 :

The null and alternative hypothesis is

H0 : p = 0.39

Ha : p > 0.39

= 0.48

1 - P0 = 0.61

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.48 - 0.39 / [(0.39 * 0.61) / 250]

z = 2.92

The test is one-tailed

P-value = 0.0018

The level of significance () = 0.02

P-value >

Fail to reject the null hypothesis.

There is insufficient evidence to support the claim that the percentage is actually more than the reported percentage.