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 and t 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 56.6 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed.

Is the company making acceptable tennis balls?

Question

Mathematics

Hahn

25 February, 13:45

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 and t 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 56.6 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed.

Is the company making acceptable tennis balls?

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Answers (1)

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Ruby Kim · Answer 1

Step-by-step explanation:

Let X be the average of tennis balls.

mu = 55.4 inches

Hypotheses:

H_0: x bar = 55.4//

H_a: x bar / neq 55.4

(Two tailed test at 10% significance level)

n = 25: x bar = 56.6 and s = 0.25

STd error = s/sqrt 25 = 0.05

Mean diff = 56.6-55.4 = 1.2"

t statistic = 1.2/0.05 = 24

df = 24

t critical value = ±1.318

Since t statistic lies outside this we reject null hypothesis

The company does not manufacture acceptable tennis balls and this is evidence at 90% confidence interval