Question

The fill volume of a random sample 40 cans of Coke were found to have a mean of x⎯=12.15 with standard deviation of =0.09. Find the value of the test statistic z for evaluating the null hypothesis =12. What is the test statistic?

Answer 1

The test statistic z used for evaluating the null hypothesis that the true mean fill volume of cans of Coke is 12 ounces is found to be 10.56, using the formula Z = (μ - μ0) / (s / √n) where the sample mean is 12.15, the hypothesized mean is 12, the standard deviation is 0.09, and sample size is 40.

Step-by-step explanation:

The question asks to find the value of the test statistic z for evaluating the null hypothesis that the true mean fill volume (μ) of cans of Coke is 12 ounces, based on a sample with a mean (μ) of 12.15 and a standard deviation (s) of 0.09 for 40 cans. To calculate the z-score, we use the formula:

Z = (μ - μ0) / (s / √n)

where μ is the sample mean, μ0 is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. Substituting the given values into this equation:

Z = (12.15 - 12) / (0.09 / √40)

Z = (0.15) / (0.09 / 6.3246)

Z = 0.15 / 0.0142

Z = 10.56

This z-score is far beyond the typical cutoff values used in hypothesis testing, usually around 1.96 or 2.58 for a 95% or 99% confidence level, suggesting strong evidence against the null hypothesis in favor of the alternative hypothesis that the true mean is different from 12 ounces.