Question

Tennis Ball Manufacturing A company manufactures tennis balls. When the balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean bounce height to be 55.5 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between and , then the company will be satisfied that it is manufacturing acceptable tennis balls. For a random sample, the mean bounce height of the sample is 56.0 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Explain.

Accepted Answer

Step 1: Identify the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is that the mean bounce height is 55.5 inches (H₀: μ = 55.5), and the alternative hypothesis is that the mean bounce height is not 55.5 inches (H₁: μ ≠ 55.5). Step 2: Calculate the test statistic (t-value) using the formula: t = x̄ - μsn, where x̄ is the sample mean (56.0), μ is the population mean (55.5), s is the sample standard deviation (0.25), and n is the sample size (25). Step 3: Determine the degrees of freedom (df) for the t-distribution. The degrees of freedom are calculated as df = n - 1, where n is the sample size (25). Step 4: Compare the calculated t-value to the critical t-values for the given significance level (not provided in the problem, but typically 0.05 for a two-tailed test). If the calculated t-value falls within the range of the critical t-values, the null hypothesis is not rejected, and the company is manufacturing acceptable tennis balls. Otherwise, the null hypothesis is rejected. Step 5: Conclude whether the company is manufacturing acceptable tennis balls based on the comparison in Step 4. If the t-value is within the acceptable range, the company is meeting its quality standards; otherwise, it is not.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Sampling Distribution

Hypothesis Testing

Confidence Intervals