**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

**2.**

**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.

**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=0Can (each) null hypothesis be rejected at the 5% significance level (use a two-sided test)?

ii) Ho: mean=5

iii) Ho: mean=10