1. Countrygirl Makeup is a line of facial products marketed to young women, ages sixteen to twenty four. Although successful when introduced in 1990, in recent years Countrygirl sales have eroded. An independent research firm was commissioned to gather information about the ages of the current users. A nationwide random sample of 50 users yielded the following ages. (2.5 points)

[Please note: Age is quantitative data type of continuous , and ratio level of measurement. Therefore, in categorizing ages of respondents into age groups, you must understand that a respondent selected at random, does not attain a particular age until his or her birthday for that particular age is attained . For example, you are not 20 until you turn 20 on your 20 ^th birthday. Therefore, an observation of 19.4 (say!) , would not belong to an age group of 20 years or above .]

19.4 31.3 22.7 27.6 27.9 30.1 23.1 26.4 32.1 22.5

28.2 25.7 33.8 28.9 18.6 26.8 30.5 34.0 21.6 28.2

32.2 27.3 17.5 23.0 32.8 36.0 29.1 42.7 30.5 39.0

26.2 33.2 36.3 22.7 43.1 28.7 26.3 38.6 24.1 21.3

32.1 28.7 25.8 26.0 18.7 18.2 23.9 28.2 20.2 33.1

1. Talley the data into frequency distribution, using only six classes, with the first class ranging from 15 -19 age group. Form the relative (percentage) frequency distribution! ( 1.0 point)
2. Construct a histogram, using Excel ( 1.0 point)
3. On the basis of the results of (a), and (b), if you had to tell the president of the Countrygilr, the reason why in recent years the sales has plummeted, what advice would you provide as basis for future advertising and promotion decisions?

Should the current age range of 16 to 24 years old be a good basis for the

company to base their future advertising and promotion decisions?. Explain

(0.50 point)

.

2 . In a medical study, a researcher wished to estimate the average length of time for a particular nurse-in-training to draw a series of blood specimens. A sample of 49 observations of the nurse’s work over several months yielded the following times (in minutes): (2.5 points)

7.3 6.9 15.9 5.4 13.1 9.9 8.4 9.6 4.1 11.1

12.1 14.1 11.3 10.5 4.7 5.7 5.1 10.7 7.3 9.9

12.5 7.3 6.7 7.1 8.1 5.7 16.5 10.8 11.0 8.9

13.7 10.6 7.4 8.5 4.2 15.4 8.1 11.8 9.5 6.3

5.4 3.9 12.0 13.7 10.6 6.6 9.5 8.0 9.4

1. Compute the arithmetic mean for this sample, using the formula; ( 0.75 point)
   \[\bar{X}=\frac{\sum{X}}{n}\]
2. Compute the standard deviation for this sample, using either of the following formulas; ( 0.75 point)
   \[s=\sqrt{\frac{\sum{{{(X-\bar{X})}^{2}}}}{n-1}}\] OR \[s=\sqrt{\frac{\sum{{{X}^{2}}-\frac{{{\left( \sum{X} \right)}^{2}}}{n}}}{n-1}}\]
3. What proportion of these length of time for a particular nurse-in-training to draw a series of blood specimens fall
   1. Within ±1 standard deviation of the mean? –Must show work!
      (0.25 point)
   2. Within ± 2 standard deviations of the mean? - Must show work!
      (0.25 point)
   3. Within ±3 standard deviations of the mean?- Must show work!
      (0.25 point)
4. Compare and contrast your findings in part (c) with what would be expected on the basis of the Empirical Rule. Does E.R. apply here? Explain! (0.25 point)

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