1.One wishes to construct 100 confidence intervals with confidence level 95% from an Exponential distribution with m = 10.

Step 1: Generate 100 samples of size 20 from an Exponential distribution with m = 10. Store the results in columns C5 - C24. One can achieve this using the following commands:

MTB > random 100 c5-c24;

SUBC > Exponential 10.

Each of the first 100 rows in your spreadsheet now contains a random sample of 20 observations from an Exponential distribution with m = 10.

Step 2: Label column C4 as "xbar" and use it to store the sample means of each of the 100 samples. You can compute these by using the following commands:

MTB > rmean c5-c24, c4

Step 3: Label column C2 as "lower bound" and C3 as "upper bound". These columns will store the lower and upper bounds for the confidence intervals that we compute based on each of the 100 samples. To compute the lower bound of each interval, use the command:

MTB > let c2 = c4 - 1.96*10/sqrt(20)

Likewise, to compute the upper bound of each interval, use the command:

MTB > let c3 = c4 + 1.96*c5/sqrt(20)

Step 4: We wish to determine how many of your 100 confidence intervals do contain the true mean m = 10. One can achieve this using the following command:

MTB > let c1 = (c2 <10 and c3>10)

If a confidence interval contains the mean value m = 10, the corresponding entry in column C1 will now contain a 1; otherwise, it will contain a 0. To determine how many of the intervals did contain m = 10, use the following command:

MTB > tally c1

Questions:

A. What percentage of the intervals actually did contain the true mean m = 10?

B. Based on the interpretation of a 95% confidence interval, is this the number expected? Explain why.