Question

A national publication reported that a college student living away from home spends, on average, no more than $15 per month on laundry. You believe this figure is too low and want to disprove this claim. To conduct the test, you randomly select 16 college students and ask them to keep track of the amount of money they spend during a given month for laundry. The sample produces an average expenditure on laundry of $19.36, with a population standard deviation of $3.56. Use these sample data to conduct the hypothesis test. Assume you are willing to take a 10% risk of making a Type I error and that spending on laundry per month is normally distributed in the population.

The value of the test statistic is_____and we____ reject the null hypothesisfail to reject the null hypothesis

Answer 1

Solution:

The null and alternative hypothesis are

H₀ :    15 vs H₁ : > 15

The test statistic z is

Test statistic z = = [19.36- 15]/[3.56/16] = 4.90

> sign in H₁ indicates that the test is right tailed.

p value = P(Z > z) = P(Z > 4.90) = 1 - P(Z < 4.90) = 1 - 1 = 0.0000

Given = 10% = 0.10

p value is less than

Reject the null hypothesis .

Answer :

The value of the test statistic is 4.90 and we reject the null hypothesis.