A company manufactures tennis balls When its tennis balls ar

A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 55.4 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between minus t 0.90 andt 0.90 , then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.5 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls?

Find -T 0.90=

T 0.90=

Find t-value

Solution

Set Up Hypothesis
Null, H0: U<=55.4
Alternate, H1: U>55.4
Test Statistic
Population Mean(U)=55.4
Sample X(Mean)=56.5
Standard Deviation(S.D)=0.25
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =56.5-55.4/(0.25/Sqrt(25))
to =22
| to | =22
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.318
We got |to| =22 & | t | =1.318
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 22 ) = 0
Hence Value of P0.1 > 0,Here we Reject Ho

[ANSWER]
T 0.90 = 1.318
Find t-value = 22
company making acceptable tennis balls