Question

Directions: Include all steps of hypothesis testing in your solutions to the following problems. Show all your work, including calculations of the test-statistic and the p-value. Check your answers using PHStat. Round sample percentages to two (2) decimal places; round other numbers to four (4) decimal places. Only give the Type I or Type II error if the problem asks for these errors.

1. A fitness center offers a spin class three days a week. They want to know if they should take away one of the class times. If their average attendance per class does not exceed 12 people, they will take away a class. For 8 class days, attendance was collected. The mean number of people attending was 9, with a standard deviation of 1.3. Should the fitness center take away one of the spin class sessions? Include Type I error with your solution.

Answer 1

One sample t-test to be done here

μ: mean of population

Descriptive Statistics

N	Mean	StDev	SE Mean	95% Upper Bound for μ
8	9.000	1.300	0.460	9.871

Teststatistic t =

Null hypothesis	H₀: μ = 12
Alternative hypothesis	H₁: μ < 12

T-Value	P-Value
-6.53	0.000

since p-value is less than level of significance 0.05, hence we reject null hypothesis and conclude that mean is less than 12 and the fitness center take away one of the spin class sessions.