18.07.2022 - 14:27

# 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

Question:

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 0.2 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence at the 0.10 level of significance to conclude that the true mean discharge differs from 7 ounces? Perform a two-tailed test.

a. State the null and alternative hypotheses.

b. What is the value of the test statistic?

c. What is the p-value?

d. At the 0.10 level of significance, can we conclude that the true mean discharge differs from 7 ounces?