# Name: Beyond Neanderthal and Metrosexual: Skin Care Products for a Mansuit

In studies of the showering habits of the male Homo sapiens, Proctor & Gamble found that males were accessing specialty shower products kept in the shower by their female partners. Proctor & Gamble realized that men were not necessarily Neanderthals and that even men who were not style-oriented would pay a premium for specialty products such as soap for men only. Proctor & Gamble developed and deployed the Dial for Men line of products including soaps.
1 , 2 , 3

## Part I: Basic Statistics

Table one
Dial for Men
3D
3D
3D
Full Force
Full Force
Full Force
Blue Grit
Blue Grit
Blue Grit
3D
1. _______________ What is the level of measurement for the data in table one?
2. __________ Calculate the sample size n for table one.
3. __________ Calculate the mode for table one.
4. For the data in table one, produce BOTH a frequency table AND sketch a frequency histogram chart.
5. Table two
Days
14
13
15
11
11
11
14
14
12
13
How long does a Dial for Men bar last? This section explores the duration in days a bar of Dial for Men will last. Data was gathered starting on 13 November 2010. Each bar was used by a single person. The number of days each bar of soap lasted is recorded in table two. Use the table two data for the following questions.

__________ What is the level of measurement for the data in table two?
6. __________ Calculate the sample size n.
7. __________ Calculate the minimum.
8. __________ Calculate the maximum.
9. __________ Calculate the range.
10. __________ Calculate the midrange.
11. __________ Calculate the mode.
12. __________ Calculate the median.
13. x =__________ Calculate the sample mean x.
14. sx = __________ Calculate the sample standard deviation sx.
15. __________ Calculate the coefficient of variation.
16. _________ Determine the class width. Use 4 classes (bins or intervals).
17. Fill in the following table with the class upper limits in the first column, the frequencies in the second column, and the relative frequencies in the third column
Classes (x)Frequency fRel Freq p(x)
Sums:
18. Sketch a histogram of the frequency data to the right of the table.
19. __________________ What is the shape of the distribution?
20. __________ Using the sample mean and standard deviation of the data in table two, calculate the z-score for a single bar of soap that lasts 12 days.
21. __________ Is the z-score for a single bar of soap that lasts 12 days ordinary or unusual?
22. SE = _________ Calculate the standard error of the sample mean x
23. tcritical = _________ Calculate tcritical for a confidence level c of 95%
24. E = _________ Calculate the margin of error E for the sample mean x.
25. Write out the 95% confidence interval for the population mean μ
p(_____________ < μ < ___________) = 0.95
26. _________ A study of Ivory soap found that bars of Ivory lasted an average of 12 days. Is this average within the 95% confidence interval for the duration in days for Dial for Men?

Run a hypothesis test for whether Dial for Men has a population mean duration μ = 12 days at an alpha α of 0.05.
H0: μ = 12
H1: μ ≠ 12
27. tcritical = _________ Calculate tcritical at α = 0.05.
28. t = _________ Calculate the t-statistic t.
29. p-value = _________ Calculate the p-value.
30. max c = _________ Calculate the maximum confidence that the Dial for Men does not last 12 days.
31. _____________________ At an alpha α of 5%, would you fail to reject |or| reject the null hypothesis?
32. ___________ Does Dial for Men last statistically significantly longer than Ivory soap?
Table three
Dial for MenTone
1410
139
1514
118
118
116
1412
1413
1210
13

Part II: Hypothesis Testing using the t-test
Beauty soaps for women have been around for decades. These also cost more than regular soap. Run a two sample hypothesis test as to whether there is a statistically significant difference for the duration of Dial for Men versus Tone beauty soap. Use a risk of rejecting a true null hypothesis, alpha α, of = 0.05. The data in table three is the duration in days for bars of Dial for Men and Tone.
33. _________ Calculate the sample mean duration of Dial for Men soap bars.
34. _________ Calculate the sample mean duration of Tone soap bars.
35. _________ Are the sample means for the two samples arithmetically different?
36. __________________ What is the p-value? Use the TTEST function with two tails to determine the p-value for these two independents samples.
37. __________________ Is the difference in the means statistically significant at an alpha α = 0.05?
38. __________________ Would we fail to reject | or | reject a null hypothesis of no difference in the sample means?
39. __________________ What is the maximum level of confidence we can have that the difference is statistically significant?
40. __________________ Based on the above analysis, does Dial for Men last statistically significantly longer at an alpha α of 0.05?

Part III: Linear Regression (best fit or least squares line)

Data table

DayMass (g)
0112
1103
291
381
470
556
648
736
823
916
109
113
120
41. _________ Calculate the slope of the linear regression (best fit line).
42. _________ Calculate the y-intercept of the linear regression (best fit line).
43. _________ Is the relation positive, negative, or neutral?
44. _________ Calculate the linear correlation coefficient r for the data.
45. ______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
46. ______________ Determine the coefficient of determination.
47. ______________ What percent in the variation in the day "explains" the variation in mass?
48. _________ The above data is for a bar of Dial for Men 3D soap. In a separate study, Ivory soap was found to have a linear regression of y = -10x + 127. That is, mass = -10 * day + 127. What will be the mass of the Ivory on the fifth day (day = 5 )?
49. _________ Using the Ivory soap linear regression equation above, y = -10x + 127 or mass = -10 * day + 127, what will be the day on which the Ivory will have a mass of 37 grams?