A company manufactures tennis balls. When its tennis balls are dropped onto a co

Question

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 55.5 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between -t_0.98 and t_0.98, 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 56.1 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_0.98 and t_0.98. -t_0.98 = t_0.98 = (Round to three decimal places as needed.) Find the t-value. t-value = Is the company making acceptable tennis balls? Choose the correct answer below. A. The tennis balls are acceptable because the t-value falls between -t_0.98 and t_0.98. B. The tennis balls are not acceptable because the t-value falls outside -t_0.98 and t.98. C. The sample is not large enough to determine if the tennis balls are acceptable.

Explanation / Answer

Degree of freedom = 25-1 = 24

Critical values of t:

Asuming a two tail test

-t0.98 = - 2.492

t0.98 = 2.492

Confidence interval:

The 98% confidence interval is 55.975 < < 56.225

So, mean of 55.5 doesn't lie in Confidence interval, balls are not acceptable.

B option. Not acceptable. or the sample size is also small.

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