Question

According to one survey taken a few years ago, 32% of American households have attempted to reduce their long-distance phone bills by switching long-distance companies. Business researchers want to test to determine if this figure is still accurate today. The researchers have taken a new survey of 85 American households who have tried to reduce their long-distance bills. Suppose that of these 85 households, 26% say they have tried to reduce their bills by switching long-distance companies. Is there enough evidence to state a significantly different proportion of American households are trying to reduce long-distance bills by switching companies? Let α = 0.05.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.32

H_a : p 0.32

= 0.26

P₀ = 0.32

1 - P₀ = 1 -0.32 =0.68

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.26-0.32 / [0.32(1-0.32) / 85]

= -1.185

P(z <-1.185 ) = 0.2266

P-value = 0.2266

= 0.05

p=0.2266 ≥ 0.05, it is concluded that the null hypothesis is not rejected.

Reject the null hypothesis .

here is not enough evidence to claim that the population proportion pp is different than p₀, at the α=0.05 significance level.