How to find y bar and s. How to calculate an interval. How to find a percentage of scores in the data set that fall within the interval?

Question

Sanitation inspection of cruise ships. Refer to the

Centers for Disease Control and Prevention study

of sanitation levels for 169 international cruise

ships, Exercise 1.23 (p. 18). (Recall that sanitation

scores range from 0 to 100.)

(a) Find y bar and s for the 169 sanitation scores.

(b) Calculate the interval y bar +- 2s.

(c) Find the percentage of scores in the data set

that fall within the interval, part b. Does the

result agree with the rule of thumb given in

this section?

Answer 1

Hello Felix,

Given the size of the data set, I recommend using statistical software, excel with an analysis toolpak installed, or just excel. I copied the data you wrote here onto a word document and saved it as a .txt file. I then imported the data into excel and organized it in a column. The following excel formulas may be used:

For y-bar (the mean of the data) = sum(a2:a170) / 169 = 95 OR y-bar = average(a2:a170) = 95

For s (standard deviation) = stdev.s(a2:a170) = 5

Thus, (ybar - 2s, ybar + 2s) = (95 - 2*5, 95 + 2*5) = (85, 105)

Sort your data in ascending order and count the number of values that lie in the interval (85, 105) and then divide by 169. This results in approximately 97.6% of the values lying within two standard deviations of the mean.

Assuming the rule of thumb given in this section is that 95% of the values should lie within two standard deviations of the mean, make a statement comparing 97.6% with the rule of thumb.

I expect you to fill in the details to support these results. I hope this helps.