Question

a company manufactures tennis balls. when its tennis balls are dropped onto a concrete surface from a height of 100 inches, the bounce upward is 54.9 inches. this average is maintained by periodically testing random samples of 25 tennis balls. if the t - value falls between - t_{0.95} and t_{0.95}, 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_{0.95} and t_{0.95}.

• t_{0.95}=-2.064

t_{0.95}=2.064
(round to three decimal places as needed.)
find the t - value.
t - value=

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 25\). So \(df=25-1=24\).

Step2: Find the t - value

We are looking for \(-t_{0.95}\) with \(df = 24\). Using the t - distribution table or a statistical software, for a one - tailed test with \(\alpha=0.05\) and \(df = 24\), the value of \(t_{0.95}\) is \(1.711\). But since we want \(-t_{0.95}\), the value is \(- 1.711\).

Answer:

\(-1.711\)