A sample of 25 households in Prolific City revealed a mean of 7.5 residing members and a standard deviation o?

Question

A sample of 25 households in Prolific City revealed a mean of 7.5 residing members and a standard deviation of 3. If the mean household size for the nation is 4.2, what is the value of the test statistic?

Answer 1

Nothing, because the idea of assuming that household size is normally distributed is idiotic.

In a normal (Gaussian distribution) 0.5% of the population are more than 2.5 standard deviations below the mean.

http://en.wikipedia.org/wiki/Normal_distribution

Do you really believe that 1 out of 200 households in Prolific City have a size less than 0? Does your teacher really believe it?

In any case, if you have to do this stupid problem, take a look at:

http://en.wikipedia.org/wiki/Sample_size
http://en.wikipedia.org/wiki/Standard_error_(statistics)

The bottom line is that the households in Prolific City are not average.