Question

A publisher reports that 36% 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 320 found that 30% of the readers owned a laptop. Is there sufficient evidence at the 0.010 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

To Test :-

H0 :- P = 0.36
H1 :- P < 0.36

Step 2

P = X / n = 96/320 = 0.3
Test Statistic :-
Z = ( P - P0) / √(P0 * q0 / n)
Z = ( 0.3 - 0.36 ) / √(( 0.36 * 0.64) /320)
Z = -2.24

Step 3

It is one tailed test

Step 4

P value = P ( Z < -2.2361 ) = 0.0127 ( From Z table )

Step 5

α = 0.01

Step 6

Reject null hypothesis if P value < α = 0.01
Since P value = 0.0127 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Step 7

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