Question

publisher reports that 38% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually above the reported percentage. A random sample of 400 found that 44% of the readers owned a laptop. Is there sufficient evidence at the 0.05 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 test

One-Tailed Test

or

two-tailed test

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.

Reject Null Hypothesis

OR

Fail to Reject Null Hypothesis

Step 7 of 7:

State the conclusion of the hypothesis test.

There is sufficient evidence to support the claim that the percentage of readers who own a laptop is above 38%.

OR

There is not sufficient evidence to support the claim that the percentage of readers who own a laptop is above 38%.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.38

H_a : p > 0.38

$\hat p$ = 0.44

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.44 - 0.38 / [$\sqrt$(0.38 * 0.62) / 400]

Test statistic = 2.47

One tailed test .

P-value = 0.0067

The level of significance = $\alpha$ = 0.05

P-value < $\alpha$

Reject the null hypothesis .

There is sufficient evidence to support the claim that the percentage of readers who own a laptop is above 38%.