Problem set 1:  Mean, variance, standard deviation, confidence intervals and t-test of an hypothesis.

1.  Compute, by hand (and show your work), the mean, variance and standard deviation for the following data:
observation    data
    1                 10
    2                 11
    3                   9

a) Use Excel to generate a random variable, with 31 observations, a mean of 10 and a standard deviation of 1.

To create a random variable in excel, use "data", "data analysis" and "random number generator". 
The number of variables should be 1, number of random numbers should be 31, distribution should be normal, mean should be 10 and standard deviation should be 1.  NOTE: In "Random Seed" type in any combination of three numbers.  Then specify the output range for the random numbers.
If you don't see 'data analysis' you'll have to install it, Excel may not have installed it automatically.
b) use Excel to compute the mean, variance (use the function 'var') and the standard deviation (use the function 'stddev') for the generated data in (a).

c) construct a 95% and 99% confidence intervals for the computed mean.  Use table B-1 in the textbook to find the (two-sided) t-value needed to construct the confidence intervals and make sure you use the appropriate degrees of freedom.

d)  Use the t-test, given in the textbook on p.563, to test each of the following null hypothesis:

i)    Ho: mean=0
ii)   Ho: mean=5
iii)  Ho: mean=10
Can (each) null hypothesis be rejected at the 5% significance level (use a two-sided test)?