Of dishes, soap, and rice cookers ♨ Name:

Dishes
72
34
53
53
55
83
47
62
50
63
68
67
29
69
65
51
65
60
69
33
54
55
53
53
46
49
58
38

Part I: Basic Statistics

"The data was gathered by recording the sum of dishes washed after every meal time. Upon taking the task washing these dishes – cups, plates, forks-spoons-knives, cooking utensils, plastic ware, pots, pans, and bowls, – recorded how many of each category were washed each day." — KH.

Data sheet

  1. _________ What level of measurement is the data?
  2. _________ Determine the sample size n.
  3. _________ Determine the minimum.
  4. _________ Determine the maximum.
  5. _________ Calculate the range.
  6. _________ Calculate the midrange.
  7. _________ Determine the mode.
  8. _________ Determine the median.
  9. _________ Calculate the sample mean x.
  10. _________ Calculate the sample standard deviation sx.
  11. _________ Calculate the sample Coefficient of Variation.
  12. _________ Determine the class width. Use five classes (bins or intervals).
  13. 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:
  1. Sketch a histogram of the relative frequency data.
  2. __________________ What is the shape of the distribution?
  3. __________________ On 29 January 2010 the KH home washed 72 dishes Use the sample mean x and sample standard deviation sx above to calculate the z-score for 72 dishes .
  4. _________ Is the z-score for 72 dishes an ordinary or extraordinary value?
  5. __________________ On 10 February 2010 the KH home washed 29 dishes Use the sample mean x and sample standard deviation sx above to calculate the z-score for 29 dishes .
  6. _________ Is the z-score for 29 dishes an ordinary or extraordinary value?
  7. _________ Calculate the standard error of the sample mean x
  8. _________ Find tcritical for a confidence level c of 95%
  9. _________ Determine the margin of error E for the sample mean x.
  10. Write out the 95% confidence interval for the population mean μ
    p(_____________ < μ < ___________) = 0.95
  11. _________ In other homes an average of 50 items are washed nightly. Based on the confidence interval above, is the number of dishes washed in the KH home statistically significantly different than μ = 50?
  12. ___________ Using the KH sample mean and a population mean μ = 50 determine the t-statistic.
  13. ___________ Using the KH sample mean and a population mean μ = 50 determine the p-value.
  14. ___________ Using the KH sample mean and a population mean μ = 50 determine the maximum confidence c interval for which the difference is statistically significant.

Part II: Hypothesis Testing using the t-test

In part two you will run a two sample hypothesis test on whether there is a statistically significant difference between two samples using a risk of a type I error alpha α = 0.05 The sample data is the price for three bar packs of four ounce bath soap at two stores. Use a two-tailed t-test for two samples to determine whether the mean price for these bath soap packs is statistically significantly different.

Ace CommercialPriceBlue NilePrice
Coast Pacific Force3.75Coast Pacific Force3.65
Dial Gold3.75Dial for Men 3D odor defense3.65
Dial Mountain Fresh3.75Dial White tea and vitamin E3.65
Dial Spring Water3.75Zest Ocean Energy3.35
Dial Tropical Escape3.75
Dial White3.75
Irish Spring4.25

Partial solution set

statvaluestatvalue
n 7n 4
mean 3.82mean 3.58
stdev 0.19stdev 0.15
ttest 0.05 max c 0.95
  1. _________ Calculate the sample mean price for the soap at Ace Commercial.
  2. _________ Calculate the sample mean price for the soap at Blue Nile.
  3. _________ Are the sample means for the two samples mathematically different?
  4. __________________ What is the p-value? Use the TTEST function with two tails to determine the p-value for this two sample data.
  5. __________________ Is the difference in the means statistically significant at a risk of a type I error alpha α = 0.05?
  6. __________________ Would we fail to reject | or | reject a null hypothesis of no difference in the sample means?
  7. __________________ What is the maximum level of confidence we can have that the difference is statistically significant?
  8. __________________ Based on the means, is the bath soap at one of the stores statistically significantly less expensive?

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

Rice Cooker data background rectangle major grid lines axes x-axis and y-axis linear regression line data points as circles text layers Rice Cooker data April 2010 Cups Power (W) y-axis labels 200 230 260 290 320 350 380 410 440 470 500 x-axis labels 3 4 6 7 8 10 11 12 13 15 16

Data table

BrandCupsPower (W)
Black and Decker3200
Black and Decker6300
Edelweiss6300
Panasonic6310
Panasonic10450
Black and Decker16500
Edelweiss12500

The table provides data on the maximum capacity of a rice cooker in cups of cooked rice versus the power consumed in Watts (W) by the rice cooker.

  1. _________ Calculate the slope of the linear regression (best fit line).
  2. _________ Calculate the y-intercept of the linear regression (best fit line).
  3. _________ Is the relation between cups and power positive, negative, or neutral?
  4. _________ Calculate the linear correlation coefficient r for the data.
  5. ______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
  6. ______________ Determine the coefficient of determination.
  7. ______________ What percent in the variation in cups "explains" the variation in power?
  8. _________ Use the slope and intercept to predict the power that would be consumed by a rice cooker with an 8 cup capacity.
  9. _________ Use the slope and intercept to determine the cooked rice capacity for a 400 Watt rice cooker.