D. We are now about to conduct an experiment where 1,000 random samples of size n = 100 are taken from a Bernoulli population with p = .04. For each sample we will compute the sample proportion p and the confidence limits for the normal theory 95% confidence interval estimate of p. We will

then count how many of the intervals covered the population parameter p = .04.

We generate the counts x for the 1,000 random samples of size n = 100 directly as follows. Use Data > Generate Random Data with "Binomial" distribution selected to get 1,000 x's (stored in 1 column, 1000 rows) generated from the binomial distribution with 100 trials and event probability of 0.04 and rename the new column xgen2. Use Data > Formula to determine the sample proportions p = x/100; specifically, calculate the

expression xgen2/100 and rename the new column pgen2.

Use Data > Formula to calculate the LCL and the UCL based on sample size n = 100 and the sample

proportions p that are stored in Column pgen2. For LCL, calculate the expression pgen2 - 1.960*( pgen2*(1- pgen2)/100)^.5 and rename the new column LCL2. In a similar manner, calculate the UCL's using expression pgen2 + 1.960*( pgen2*(1 - pgen2)/100)^.5 and rename UCL2.

Copy the values xgen2, pgen2, LCL2 and UCL2 from your first 10 CI's of your MTB computer worksheet into columns 2 - 5 of Table 2 below and indicate in column 6 whether the CI covers the population rate p = .04. (Use two decimal places for pgen2 and three decimal places for LCL2 and UCL2.)

Table 2. CI results for p = .04 (n = 100)

Normal theory CI

Sample xgen2 pgen2 LCL2 UCL2 Cover .04? (Yes or No)

1

2

3

4

5

6

7

8

9

10

For the first row of Table 2, enter the values as responses to questions 17 and 18:

17. xgen2=______________

18. pgen2=______________

19. Out of the first 10 intervals recorded in Table 2, how many cover .04?___

Now we will check all 1,000 samples to see in how many cases the CI covers p = .04. Use Data > Formula and the statement sum(LCL2 < .04 and .04 < UCL2) to determine the number of CI's that covered p. Rename the resulting column Coverage2. Express the result as a percentage.

20. Coverage=____________ For LON-CAPA submission, enter a number between 0 and 100 without % symbol.