Question

A coin-operated drink machine was designed to discharge a mean of 8 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 12 randomly chosen cups of coffee from the machine were recorded. The sample mean arfi sample standard deviation were 7.94 fluid ounces and 0.27 fiuld ounces, respectively, If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 8 fluid ounces? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate-computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0​ and the alternative hypothesis H1​. (b) Determine the type of test statistic to use: (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or mere decimal places.)

Answer 1

In this hypothesis test, the null hypothesis states that the population mean discharge is equal to 8 fluid ounces. The alternative hypothesis states that the population mean discharge differs from 8 fluid ounces. A Z-test statistic is used to determine the test statistic, which is calculated to be -3.050. The critical values for the test are -1.96 and 1.96.

Step-by-step explanation:

(a) Null hypothesis: The population mean discharge, μ, is equal to 8 fluid ounces.
Alternative hypothesis: The population mean discharge, μ, differs from 8 fluid ounces.

(b) Type of test statistic to use: Z-test statistic.

(c) Value of the test statistic: The test statistic can be calculated by (sample mean - population mean) / (sample standard deviation / square root of sample size). In this case, the test statistic is (7.94 - 8) / (0.27 / sqrt(12)) = -3.050.

(d) Two critical values: The critical values can be calculated using the significance level and the test statistic distribution. In this case, since it is a two-tailed test with a significance level of 0.05, the critical values are -1.96 and 1.96.