Question

A publisher reports that 30% of their readers own a particular make of car. 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 37% of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim

Answer 1

we will fail to reject the null hypothesis and conclude that there's insufficient evidence to support the claim that the percentage is actually more than the reported percentage

Explanation:

We are given;

Population proportion; p = 30% = 0.3

Sample proportion; p^ = 37% = 0.37

Sample size; n = 100

Let's define the hypotheses;

Null hypothesis; H0: p ≤ 0.3

Alternative hypothesis; Ha: p > 0.3

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Thus;

z = (0.37 - 0.3)/√(0.3(1 - 0.3)/100)

z = 0.07/0.04582575695

z = 1.53

From z-distribution table, at z=1.53 we have;

p-value = 1 - 0.9370 = 0.063

This p-value is greater than the significance level of 0.02 and thus we will fail to reject the null hypothesis and conclude that there's insufficient evidence to support the claim that the percentage is actually more than the reported percentage