Use excel functions to answer the questions. a) We have estimated the mean of a population to be 7. The 95% confidence interval for our estimate is 7....

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%