Question

A coin-operated drink machine was designed to discharge a mean of 9 ounces of coffee per cup. In a test of the machine, the discharge amounts in 16 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.85 ounces and 0.25 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, H, differs from 9 ounces? Perform a two-talled test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. 0 р The null hypothesis: x s The alternative hypothesis: 몸 DO DO 020 The type of test statistic: (Choose one) DOO The value of the test statistic: (Round to least three decimal places.) 0 X 5 ? The two critical values at the Save For Later Submit Agent Check

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test: Mean of population LH : H = 9 HAN=9 Hypothesis test results: Mean Sample Mean Std. Err. DF T-Stat P-value 8.85 0.0625 15 -2.4 0.0298

From above output:

H₀ : μ = 9

H₁ : μ ≠ 9

Type: t; Degrees of freedom = 15

Test statistic = -2.4

Critical values = -1.753 and 1.753

Conclusion: Yes