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 54.8 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the​ t-value falls between minust 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 56.9 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis​ balls?

Answer 1

A one-sample t-test was conducted to determine if the tennis balls had an acceptable mean bounce height. The calculated t-value was significantly outside the acceptance region, leading to the rejection of the null hypothesis and concluding the company is not manufacturing acceptable tennis balls.

Step-by-step explanation:

To determine if the company is producing tennis balls that bounce to an acceptable average height, we need to conduct a one-sample t-test since the population standard deviation is unknown and the sample size is less than 30. The null hypothesis (H0) for this t-test is that the mean bounce height is 54.8 inches. The alternative hypothesis (Ha) is that the mean bounce height is not 54.8 inches. Thus, we are performing a two-tailed test.

The test statistic (t) is calculated as:

t = (sample mean - population mean) / (sample SD/√n)

t = (56.9 - 54.8) / (0.25/√25) = 42

With 24 degrees of freedom (n-1 for a sample size of 25), if we look at a t-distribution table, we find that a t-value of 42 is far outside the acceptance region of -0.95 to 0.95. Therefore, we reject the null hypothesis, concluding that the company is not producing acceptable tennis balls in terms of the mean bounce height specification.

Answer 2

Yes the company is making them correct boss