Question

A publisher reports that 71%  of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually less than the reported percentage. A random sample of 280 found that 65% of the readers owned a particular make of car. 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 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

1)

H0: p = 0.71

Ha: p < 0.71

2)

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.65 - 0.71) / sqrt [ 0.71 ( 1 - 0.71) / 280 ]

= -2.21

3)

This is one tailed test

4)

p-value = P(Z < z)

= P(Z < -2.21)

= 0.0136

5)

Level of significance = 0.02

6)

Decision = since p-value < 0.02 level, Reject the null hypothesis.

7)

We conclude that we have sufficient evidence to support the claim that the percentage is actually

less than the reported percentage