In: Statistics and Probability
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.
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.