Question

A publisher reports that 62% 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 130 found that 70% 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 :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.62

H_a : p > 0.62

= 0.70

n = 130

P₀ = 0.62

1 - P₀ = 0.38

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.70 - 0.62 / [(0.62 * 0.38) / 130]

= 1.88

P(z > 1.88) = 1 - P(z < 1.88) = 0.0301

P-value = 0.0301

= 0.02

P-value >

Fail to reject the null hypothesis .

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