Question

A frequenter of a pub had observed that the new barman poured in average 0.47 liters of beer into the glass with a standard deviation equal to 0.09 liters instead of a half a liter with the same standard deviation. The frequenter had used a random sample of 47 glasses of beer in his experiment. Consider the one-sided hypothesis test for volume of beer in a glass: H0: u=0.5 against H1: u<0.5. Determine the P-value of this test.
Round your answer to four decimal places (e.g. 98.7654).

Answer 1

Answer:

P-value = 0.0011

Explanation:

Formula for the test statistic is;

z = (x¯ - μ)/(σ/√n)

We have;

Sample mean;x¯ = 0.47

Population mean; μ = 0.5

Standard deviation; σ = 0.09

Sample size; n = 47

Thus;

z = (0.46 - 0.5)/(0.09/√47)

z = -3.05

From z-distribution table attached, the p-value corresponding to z = -3.05 is;

P = 0.00114

To four decimal places gives;

P-value = 0.0011