1) Suppose I take a random sample of size 10 and the histogram created from this data is approximately normal
(so my conditions will be met) and the population standard deviation is not known.
a) Find the multiplier for a 90% confidence interval for the mean time on the Internet. Give correct notation
(t or Z).
b) Find the multiplier for a 95% confidence interval for the mean time on the Internet.
c) What happens to the value of the multiplier when the confidence level increases?
2) I decided to take a larger random sample than I mentioned in part 1 (one of my smarter decisions.) The
histogram of the data is still approximately normal but remember that I do not know the population standard
deviation (so my conditions will be met), and the population standard deviation is not known.
a) Find the multiplier for a 98% confidence interval for the mean time on the Internet, if the sample size is
20. Give correct notation (t or Z).
b) Find the multiplier for a 98% confidence interval for the mean time on the Internet, if the sample size is 30.
c) What happens to the value of the multiplier when the sample size increases?
d) When the sample size increases, does the t multiplier get closer or further away from the Z multiplier
(using the same confidence level for both)?
3) I now get really smart and decide to take a random sample of size 100 for this problem. Find the multiplier
for a 95% confidence interval for the mean time on the Internet. Give correct notation. (Note: when using the
table and the df is not on it, we use the next lower df that is on the table NOT the closest one. We do this in
order to be \"conservative\" - we would rather overestimate the critical value than underestimate it.)
b) Does the histogram of the data need to look approximately normal this time? Explain why or why not.
4) Suppose I somehow found out the population standard deviation. If I now find a 99% confidence interval
using a random sample of 81 students, what is the value of the multiplier for this interval? Show correct
otation.
