Question

A publisher reports that 30% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually less than the reported percentage. A random sample of 130 found that 20% of the readers owned a laptop. Is there sufficient evidence at the 0.01 level to support the executive's claim

Step 1 State the null and alternative hypotheses.

Step 2 Find the value of the test statistic. Round your answer to two decimal places.

Step 3 Specify if it is one tailed or two tailed

Step 4 Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 Make the decision to reject or fail to reject the null hypothesis.

Step 6 State the conclusion of the hypothesis test.

Answer 1

Solution :

Given that,

= 0.30

1 - = 0.70

n = 130

Level of significance = = 0.01

Point estimate = sample proportion = = 0.20

Step 1

The null and alternative hypothesis is,

Ho: p = 0.30

Ha: p < 0.30

Step 2

Test statistics

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

= ( 0.20 - 0.30) / (0.30*0.70) /130

= 2.49

Step 3

This a left (One) tailed test.

Step 4

P_value = P(Z < 2.49 )

= 0.9936

Step 5

The p-value is p = 0.9936, and since p = 0.9936 > 0.01, it is concluded that fail to reject the null hypothesis.

Step 6

It is concluded that

It is concluded that fail to reject the null hypothesis. Therefore, there is no enough evidence to claim that the percentage is actually less than the reported percentage.at the α = 0.01 significance level.