Use excel functions to answer the questions...

a) We have estimated the mean of a population to be 7.5. The 95% confidence interval for our estimate is 7.5 3.5. Are the following hypotheses accepted or rejected at the 5% level of significance. And can we say whether they are accepted or rejected at the 1% level of significance?

i) mean = 0 ?

ii) mean = 3 ?

iii) mean = 8 ?

iv) mean = 12 ?

In each case carry out a two-tailed test.

b) You have a sample of 15 observations on a variable X. The mean of these is 8.4 and the sample standard deviation is 5.5 per observation. Use a 5% significance level. Is this evidence consistent with population means of:

i) 0 ?

ii) 5 ?

iii) 10 ?

iv) 15 ?

In each case carry out a two-tailed test.

c) From a sample of 60 monthly returns, you calculate a sample mean return of 0.5% per month and a standard deviation of monthly returns of 1%. Construct the following confidence intervals:

i) 90%

ii) 95%

iii) 99%

iv) 99.9%