The mean wage of people living in a block of flats is said to be £400 a week. A random sample of 36 people was examined to give a sample mean of £435 and a sample standard deviation of £84.

a. (i) Set up the null and alternative hypothesis for a two-sided test of the mean.

(ii) Determine the two-sided critical values that define the regions of rejection for both a significance level of 5 per cent and 1 per cent.

(iii) Determine the test statistic.

(iv) Compare your test statistic with your critical values. Can you retain or reject the null hypothesis at both levels of significance?

b. (i) Set up the null and alternative hypothesis for a one-sided test of the mean.

(ii) Determine the one-sided critical values that define the regions of rejection for both a significance level of 5 per cent and 1 per cent.

(iii) Compare your test statistic with your critical values. Can you retain or reject the null hypothesis at both levels of significance?