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. The Safety Climate Index (SCI) measures workers’ perceptions about the safety of their work environment. A study of safe work practices of industrial workers reported mean SCI scores for workers classified by   workplace size.15 Here are the means:

Workplace size$1rn   : Fewer than$1rn    50 to 200$1rn    More than

$1rn $1rn $1rn $1rn $1rn $1rn$1rn 50 workers$1rn$1rn workers$1rn $1rn 200 workers

Mean SCI:$1rn $1rn $1rn $1rn 67.23$1rn $1rn $1rn 70.37$1rn $1rn$1rn 74.83

Assume that the standard deviation is 19 and the sample sizes are all 180. (We will discuss ways to compare three means such as

these in Chapter 12.)

(a) Calculate the 95% confidence interval for each mean.

(b) Plot the means versus workplace size. Draw a vertical line through the first mean extending up to the upper confidence limit

and down to the lower limit. At each end of the line, draw a short dash. Do the same for each of the other means.

(c) One way to adjust for the fact that we are reporting three confidence intervals is a procedure that uses a larger value of z∗

in the calculation of the margin of error. For this problem one recommendation would be to use z∗ = 2.40. Repeat parts (a)

and (b) making this adjustment. (d) Summarize your results. Be sure to include comments on the effects of the adjustment on your results.