Questions: A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 55.4 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value is significant, it means the company is not manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the tennis balls must meet certain standards, and it is assumed that the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find -t0.98 and t0.98. -t0.98=square t0.98=square (Round to three decimal places as needed.)

A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 55.4 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value is significant, it means the company is not manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the tennis balls must meet certain standards, and it is assumed that the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find -t0.98 and t0.98. -t0.98=square t0.98=square (Round to three decimal places as needed.)
Transcript text: A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 55.4 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the $t$-value is significant, it means the company is not manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the tennis balls must meet certain standards, and it is assumed that the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? \[ \begin{array}{l} \text { Find }-t_{0.98} \text { and } t_{0.98} . \\ -t_{0.98}=\square \\ t_{0.98}=\square \end{array} \] (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Determine the Critical Values

To assess whether the company is manufacturing acceptable tennis balls, we need to find the critical values for the t-distribution at the \(0.98\) significance level. The critical values are defined as follows:

\[ -t_{0.98} = -2.326 \] \[ t_{0.98} = 2.326 \]

Step 2: Interpretation of the Critical Values

The critical values \(-t_{0.98}\) and \(t_{0.98}\) represent the cutoff points for the acceptance region in hypothesis testing. If the sample mean of the bounce heights falls outside the interval \([-2.326, 2.326]\), we would reject the null hypothesis that the mean bounce height is equal to \(55.4\) inches.

Final Answer

The critical values for the t-distribution at the \(0.98\) significance level are:

\[ -t_{0.98} = -2.326, \quad t_{0.98} = 2.326 \]

Thus, the final boxed answer is:

\[ \boxed{-t_{0.98} = -2.326, \quad t_{0.98} = 2.326} \]

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