A coin-operated drink machine was designed to discharge a mean of 6 ounces of coffee per cup. In a test of the machine, the discharge amounts in 20 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 5.9 ounces and 0.18 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge, ?, differs from 6 ounces?

Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

(a) State the null hypothesis H and the alternative hypothesis H. H P H : I X S P H , : 0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 X ? (d) Find the two critical values. (Round to three or more decimal places.) and (e) At the 0.05 level of significance, can we conclude that the true mean discharge differs from 6 ounces? Yes No