PORTLAND STATE UNIVERSITY

Fariborz Maseeh Department of Mathematics & Statistics

WINTER TERM 2015

Stat 452/552 Bring results to class on Tuesday, Jan. 13

Worksheet 1.

Use MINITAB to simulate (1 − α) × 100% Z-Confidence Intervals for a

Population Mean µ and with known standard deviation σ. Step by Step MINITAB tips is given on page 2.

The formula is

.

That is,

.

Suppose n = 9 men are selected at random from a large population. Assume

the heights of the men in this population are normal, with mean µ = 69 inches

and standard deviation σ = 3 inches. Simulate the results of this selection 20

times and in each case find a 90% confidence interval for µ. Then answer the following:

1. How many of the intervals contain µ?

2. Would you expect all 20 of the intervals to contain µ? Explain.

3. Do all the intervals have the same width? Why or why not?

4. Suppose you took 95% intervals instead of 90%. Would they be narrower or wider?

5. How many of your intervals contain the value 72? The value 70? The value 69?

6. Suppose you took samples of size n = 100 instead of n = 9. Would you expect more or fewer intervals to cover 72? 70? 69? What about the

width of the intervals for n = 100? Would they be narrower or wider

than for n = 9?

7. Suppose you calculated 90% confidence intervals for 20 sets of real data. About how many of these intervals would you expect to contain µ? Could you tell which intervals were successful and which were not? Why or why not?

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