Question

A publisher reports that 69% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 310 found that 64% of the readers owned a laptop. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.

Answer 1

H₀: P = 0.69

H₁: P 0.69

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                             = (0.64 - 0.69)/sqrt(0.69 * (1 - 0.69)/310)

                             = -1.90

P-value = 2 * P(Z < -1.90)

             = 2 * 0.0287

             = 0.0574

Since the P-value is greater than the significance level(0.0574 > 0.05), so we fail to reject the null hypothesis.