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 19 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 $19.38, with a population standard deviation of $3.53. 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.

(Round your answer to 2 decimal places.)

The value of the test statistic is and we

fail to reject the null hypothesis or reject the null hypothesis

.

Answer 1

Step 1:

Ho:  

Ha:

Null hypothesis states that college student living away from home spends  $15 or less per month on laundry.

Alternative hypothesis states that college student living away from home spends more than $15 per month on laundry.

Step 2:

n = 19

sample mean = 19.38

population sd = 3.53

z = 5.408

Step 3:

At level of significance = 0.10, Critical Value of Z (Right Tailed): 1.28

As the z stat falls in the rejection area, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that college student living away from home spends more than $15 per month on laundry.