Question

1. In a sample of 64 Pasadena residents the mean age was 57.8 years. From the census it's known that the age has a standard deviation of 6.5 years. Find a 90% confidence interval for the population mean age. (Note: CL=0.90)

2.

The following table list the number of white mathematicians mentioned in a sample of 30 textbooks.

4	6	6	7	9	9	10	10	11
13	13	14	15	17	17	18	18	19
19	21	21	22	22	22	22	22	17
15	8	20

If it is known that the standard deviation is 5 mathematicians, find a 99% confidence interval for the population mean.

Answer 1

We would be looking at the first question here on confidence interval.

Q1) We are given the population standard deviation here, therfore we will use standard normal tables, to get the critical value here.

For 90% confidence level, we have from standard normal tables:
P(-1.645 < Z < 1.645) = 0.9

therefore the confidence interval for the population mean here is computed as:

This is the required 90% confidence interval for the population mean here.