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. Suppose that business researchers want to test to determine if this figure is still accurate today by taking a new survey of 80 American households who have tried to reduce their long-distance bills. Suppose further that of these 80 households, 25% say they have tried to reduce their bills by switching long-distance companies. Is this result enough evidence to state that a significantly different proportion of American households are trying to reduce long-distance bills by switching companies? Let α = .01

The value of the test statistic is _________ and we choose between reject the null hypothesis or fail to reject the null hypothesis   

Answer 1

Given that, sample size (n) = 80 and

sample proportion = 0.25

The null and alternative hypotheses are,

H0 : p = 0.32

Ha : p ≠ 0.32

Test statistic is,

critical values at significance level of α = 0.01 are, Z^* = ±2.575

Since, test statistic = -1.34 > -2.575, we fail to reject the null hypothesis.

Therefore, the value of the test statistic is Z = -1.34 and we choose fail to reject the null hypothesis.