Question

The label on a “two liter” bottle of soft drink indicates that it is supposed to contain 2000 milliliters (ml). However, there is some variation due to the production process; this process is known to be normally distributed with a standard deviation of 20 ml. A government inspector wants to ensure that the public is not cheated by purchasing underfilled containers. A random sample of nine containers was selected; the measurement results were: 1995, 1960, 2005, 2008, 1997, 1992, 1986, 1972 and 2013 ml. Is this convincing evidence (using a 5% significance level, α = .05) that the containers are underfilled?

a) State (using symbols) the null and alternative hypotheses.

b) Identify and calculate the test statistic.

c) Determine the P-value.

d) Reach a decision and present the conclusion.

Answer 1

Null Hypothesis, 2000

Alternative Hypothesis, 2000

Here, sample mean, 1992, Population std. dev., 20, Sample size, n = 9

Here the significance level, 0.05. This is right tailed test; hence rejection region lies to the right. -1.64 i.e. P(z < -1.64) = 0.05

Reject H0 if test statistic, z < -1.64

Test statistic,

z = (1992 - 2000)/(20/sqrt(9))

z = -1.2

P-value = P(z < -1.2)

P-value = 0.1151

As p-value is greater than 0.05, fail to reject H0

There is not sufficient evidence to conclude that the mean is less than 2000 ml (i.e. underfilling)