"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.
_________ Calculate the sample standard deviation sx.
_________ Calculate the sample Coefficient of Variation.
_________ Determine the class width. Use five classes (bins or intervals).
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 f
Rel Freq p(x)
Sums:
Sketch a histogram of the relative frequency data.
__________________ What is the shape of the distribution?
__________________
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 .
_________ Is the z-score for
72 dishes an ordinary or extraordinary value?
__________________
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 .
_________ Is the z-score for
29 dishes an ordinary or extraordinary value?
_________ Calculate the standard error of the sample mean x
_________ Find tcritical for a confidence level c of 95%
_________ Determine the margin of error E for the sample mean x.
Write out the 95% confidence interval for the population mean μ
p(_____________ < μ < ___________) = 0.95
_________
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?
___________
Using the KH sample mean and a population mean μ =
50
determine the t-statistic.
___________
Using the KH sample mean and a population mean μ =
50
determine the p-value.
___________
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 Commercial
Price
Blue Nile
Price
Coast Pacific Force
3.75
Coast Pacific Force
3.65
Dial Gold
3.75
Dial for Men 3D odor defense
3.65
Dial Mountain Fresh
3.75
Dial White tea and vitamin E
3.65
Dial Spring Water
3.75
Zest Ocean Energy
3.35
Dial Tropical Escape
3.75
Dial White
3.75
Irish Spring
4.25
Partial solution set
stat
value
stat
value
n
7
n
4
mean
3.82
mean
3.58
stdev
0.19
stdev
0.15
ttest
0.05
max c
0.95
_________ Calculate the sample mean
price for the soap at Ace Commercial.
_________ Calculate the sample mean
price for the soap at Blue Nile.
_________ Are the sample means for the two samples mathematically different?
__________________
What is the p-value? Use the TTEST function with two tails
to determine the p-value for this two sample data.
__________________ Is the difference in the means statistically significant
at a risk of a type I error alpha α = 0.05?
__________________ Would we fail to reject| or |reject a null hypothesis of no difference
in the sample means?
__________________ What is the maximum level of confidence we can have that the
difference is statistically significant?
__________________
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)
Data table
Brand
Cups
Power (W)
Black and Decker
3
200
Black and Decker
6
300
Edelweiss
6
300
Panasonic
6
310
Panasonic
10
450
Black and Decker
16
500
Edelweiss
12
500
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.
_________ Calculate the slope of the linear regression (best fit line).
_________ Calculate the y-intercept of the linear regression (best fit line).
_________ Is the relation between cups and power positive, negative, or neutral?
_________ Calculate the linear correlation coefficient r for the data.
______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
______________ Determine the coefficient of determination.
______________ What percent in the variation in
cups
"explains" the variation in
power?
_________ Use the slope and intercept to predict
the power that would be consumed by a rice cooker with an
8 cup capacity.
_________ Use the slope and intercept to determine
the cooked rice capacity for a 400 Watt rice cooker.