A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. The discharge amounts in 14 randomly chosen cups of coffee from the machine were recorded, and the sample mean and sample standard deviation were 7.14 ounces and

a. The null hypothesis is that the true mean discharge is 7 ounces (?=7). The alternative hypothesis is that the true mean discharge differs from 7 ounces (??7). b. The test statistic is calculated as (sample mean - population mean)/(standard deviation/sqrt(sample size)) = (7.14 - 7)/(0.2/sqrt(14)) = 2.12. c. The p-value can be found using a t-distribution table or calculator. Using a two-tailed test with 13 degrees of freedom (n-1), the p-value is 0.052. d. At the 0.10 level of significance, we cannot conclude that the true mean discharge differs from 7 ounces because the p-value (0.052) is greater than the significance level (0.10). Therefore, we fail to reject the null hypothesis and there is not enough evidence to suggest that the mean discharge is different from 7 ounces.