From beginner to expert, IDNLearn.com has answers for everyone. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.

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

Sagot :

Answer:

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

Step-by-step 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

We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.