Question

5. People’s Choice, a monthly magazine, claimed that more than 40% of its subscribers had an annual income of $100,000 or more. In a random sample of 62 subscribers, 30 had incomes of $100,000 or more. Using a significance level of 0.10, does this information substantiate the claim of the magazine? Show all test parts to receive full credit. (15 pts)

Answer 1

5. People’s Choice, a monthly magazine, claimed that more than 40% of its subscribers had an annual income of $100,000 or more. In a random sample of 62 subscribers, 30 had incomes of $100,000 or more. Using a significance level of 0.10, does this information substantiate the claim of the magazine? Show all test parts to receive full credit. (15 pts)

One sample proportion test

Ho: P=0.40, H₁: P > 0.40

Upper tail test used

sample proportion p=30/62=0.4839

=1.348

Table value of z at 0.10 level = 1.282 (upper tail)

Rejection Region: Reject Ho if z > 1.282

Calculated z = 1.348 falls in the rejection region

The null hypothesis is rejected.

The data provide evidence to support the claim of the magazine that more than 40% of its subscribers had an annual income of $100,000 or more.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.4
Level of Significance	0.1
Number of Items of Interest	30
Sample Size	62
Intermediate Calculations
Sample Proportion	0.4839
Standard Error	0.0622
Z Test Statistic	1.3480
Upper-Tail Test
Upper Critical Value	1.2816
p-Value	0.0888
Reject the null hypothesis