Question

A publisher reports that 79% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually more than the reported percentage. A random sample of 100 found that 89% of the readers owned a personal computer. Is there sufficient evidence at the 0.02 level to support the executive's claim?

Answer 1

H0: Null Hypothesis: P = 0.79

HA: Alternative Hypothesis: P>0.79

P = Population Proportion = 0.79

So,

Q = 1 - P = 0.21

n = Sample Size = 100

p = Sample Proportion = 0.89

SE =

=

Test statistic is:

Z = (0.89 - 0.79)/0.0407 = 2.46

= 0.02

One Tail - Right Side Test

From Table, critical value of Z = 2.05

Since the calculated value of Z = 2.66 is greater than critical value of Z = 2.05, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the percentage of owning a personal computer is more than 79%.