A coin-operated coffee machine was designed to discharge 8 ounces of coffee per

Question

A coin-operated coffee machine was designed to discharge 8 ounces of coffee per cup. In a test of the machine. 20 cupfuls of coffee were drawn from the machine and measured. The number of ounces discharged for each of the cups is 7.70, 8.23, 7.86. 7.66, 7.70. 8.12, 7.80. 8.11, 8.06. 8.32, 8.00, 8.28, 8.26, 7.92, 7.65, 7.81, 8.27, 7.67, 7.89. 8.05 At the 0.02 level of significance, can we conclude (by using a sign test) that the median discharge of a cup of coffee from this machine differs from 8 ounces? Perform this hypothesis test by completing the table below. (If necessary, consult a table with critical values for the sign test.)

Explanation / Answer

Solution:

Below are the null and alternate hypothesis

H0: m = 8

H1: m <> 8 (<> represents not equals to)

The provided number of positive signs is X+ = 10 and the number of negative signs is X- = 9.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: Median of Differences = 0

Ha: Median of Differences 0

The test statistic is X = min{X+, X-} = min{10, 9}= 9

(2) Rejection Region

The critical value for the signficance level provided and the type of tail is X* = 4

(3) Decision about the null hypothesis

Since in this case X = 9 > X=4, there is not enough evidence to claim that the population median of differences is different than 0, at the 0.05 significance level.

1 7.7 0.3 2 8.23 -0.23 3 7.86 0.14 4 7.66 0.34 5 7.7 0.3 6 8.12 -0.12 7 7.8 0.2 8 8.11 -0.11 9 8.06 -0.06 10 8.32 -0.32 11 8 0 12 8.28 -0.28 13 8.26 -0.26 14 7.92 0.08 15 7.65 0.35 16 7.81 0.19 17 8.27 -0.27 18 7.67 0.33 19 7.89 0.11 20 8.05 -0.05

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