Question

In: Statistics and Probability

A publisher reports that 28% of their readers own a personal computer. A marketing executive wants...

A publisher reports that 28% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 300 found that 23% of the readers owned a personal computer. Determine the P-value of the test statistic. Round your answer to four decimal places.

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Expert Solution

Solution:

   We are given that: A publisher reports that 28% of their readers own a personal computer.

That is: p = 0.28

Sample Size = n = 300

Sample proportion =

Claim: the percentage is actually different from the reported percentage.

Step 1) State H0 and H1:

  

Vs

Step 2) Find test statistic:

Step 3) Find p-value:

p-value = 2 x P(Z < z test statistic )

p-value = 2 x P( Z < -1.93 )

Look in z table for z = -1.9 and 0.03 and find area.

P( Z < -1.93) = 0.0268

Thus

p-value = 2 x P( Z < -1.93 )

p-value = 2 x 0.0268

p-value = 0.0536

Step 4) Rejection rule: Reject H0 , if p-value < 0.05 level of significance, otherwise we fail to reject H0.

Since p-value = 0.0536 > 0.05 level of significance, we fail to reject H0.

Step 5) Conclusion: There is not sufficient evidence to support the claim that the percentage is different from the reported percentage.


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