Question

A publisher reports that 56%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 350 found that 52% of the readers owned a laptop. Is there sufficient evidence at the 0.02 level to support the executive's claim?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.56

H_a : p 0.56

= 0.52

n = 350

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.52 - 0.56 / [(0.56 * 0.44) / 350]

= -1.51

P(z < -1.51) = 0.0655

P-value = 2 * 0.0655 = 0.1310

= 0.02

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence at the 0.02 level to support the executive's claim .