Average soap consumption in a certain country is believed to be 2.5 bars per person per month. The standard deviation of the population is known to be σ = 0.8.

While the standard deviation is not believed to have changed (and this may be substantiated by several studies), the mean consumption may have changed either upward or downward.

A survey is therefore undertaken to test the null hypothesis that average soap consumption is still 2.5 bars per person per month versus the alternative that it is not. A sample of size n = 20 is collected and gives x‾ = 2.3.

The population is assumed to be normally distributed. What is the appropriate test statistic in this case? Conduct the test and state your conclusion. Use α = 0.05. Does the choice of level of significance change your conclusion? Explain.