Question

Spaulding is the leading maker for basketballs in the US. Spaulding prides itself on the quality that its basketballs have the right amount of bounce when it is taken out of the packaging. They want their product to be ready for use upon opening. The air pressure of a particular ball has a target value of 7.8 PSI. Suppose the basketballs have a normal distribution with a standard deviation of 0.25 PSI. When a shipment of basketballs arrive, the consumer takes a sample of 28 from the shipment and measures their PSI to see if it meets the target value, and finds the mean to be 7.3 PSI. Perform this hypothesis test at the 5% significance level using the critical value approach.

For you answer in this problem - give the calculated test statistic you would come up with in step 5 of the hypothesis testing process. Give answer to 3 decimal places.

Your Answer:

Question 9 options:

Answer

Answer 1

Solution:

We have to use Z test for population mean.

H₀: µ = 7.8 versus H_a: µ ≠ 7.8

We are given α = 0.05

Test statistic formula is given as below:

Z = (Xbar - µ) / [σ/*sqrt(n)]

We are given

Xbar = 7.3

µ = 7.8

σ = 0.25

n = 28

Z = (7.3 – 7.8)/[0.25/sqrt(28)]

Z = -0.5/ 0.047245559

Z = -10.5830052

Test statistic = Z = -10.583

Critical Z value = -1.96 and 1.96 (by using z-table)

Test statistic value is out of critical range -1.96 to 1.96, so we reject the null hypothesis.

There is sufficient evidence to conclude that the air pressure in the basketballs is different than 7.8 PSI.