HW11
MGMT 650
Fall 21 Week 11 Homework Questions
(Last updated 8/16/2021)
Chi Square
An analyst at a local bank wonders if the age distribution of customers coming for service at his
anch in town is the same as at a
anch located near the mall. He selects 100 transactions at random from each
anch and researches the age information for the associated customer. These are the data :
Age
less than 30 30-55 56 or older Total
In town 20 40 40 100
mall 30 50 20 100
Total 50 90 60 200
1 What is the null hypothesis if you want to check if the age patterns of customers are independent of bank location?
2 What are the expected numbers for each cell in a 3 by 3 table if the null hypothesis is true?
3 Use the chi square test to accept or reject the null hypothesis. What is the chi square test statistic?
4 What is the chi square critical value and how many degrees of freedom does it have? Assume alpha is .05.
5 What do you conclude?
ANOVA
Saeko owns a yarn shop and want to expands her color selection.
Before she expands her colors, she wants to find out if her customers prefer one
and
over another
and. Specifically, she is interested in three different types of bison yarn.
As an experiment, she randomly selected 21 different days and recorded the sales of each
and.
At the .10 significance level, can she conclude that there is a difference in preference between the
ands?
Misa's Bison Yak-et-ty-Yaks Buffalo Yarns
799 776 799
784 640 931
807 822 794
675 856 920
795 616 731
875 893 837
Total 4,735.00 4,603.00 5,012.00
6) What is the null hypothesis?
What is the alternative hypothesis?
What is the level of significance?
7) Use Tools - Data Analysis - ANOVA:Single Factor
to find the F statistic:
8) From the ANOVA output: What is the F value?
What is the F critical value?
9) What is your decision?
Explain in statistical terms
Regression
Studies have shown that the frequency with which shoppers
owse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you
owse online retailers per year?”
Age (X) Time (Y)
16 307
17 285
19 267
22 343
22 393
22 287
22 253
28 364
28 251
28 248
28 433
30 319
33 226
34 321
35 336
35 302
35 476
36 395
39 473
39 342
40 539
42 455
43 326
44 565
48 385
50 590
50 507
51 333
52 426
54 261
58 625
59 252
60 615
10) Use Data > Data Analysis > Co
elation to compute the co
elation checking the Labels checkbox.
11) Use the Excel function =CORREL to compute the co
elation. If answers for #1 and 2 do not agree, there is an e
or.
The strength of the co
elation motivates further examination.
12) a) Insert Scatter (X, Y) plot linked to the data on this sheet with Age on the horizontal (X) axis.
b) Add to your chart: the chart name, vertical axis label, and horizontal axis label.
c) Complete the chart by adding Trendline and checking boxes
Read directly from the chart:
13) a) Intercept =
b) Slope =
c) R2 =
Perform Data > Data Analysis > Regression.
14) Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the R Square in orange
15) Use Excel to predict the number of minutes spent by a 22-year old shopper. Enter = followed by the regression formula.
Enter the intercept and slope into the formula by clicking on the cells in the regression output with the results.
16) Is it appropriate to use this data to predict the amount of time that a 9-year-old will be on the Internet?
If yes, what is the amount of time, if no, why?
Cleaning Data with Outlie
17) On this worksheet, make an XY scatter plot linked to the following data:
X Y
1.01 2.8482
1.48 4.2772
1.8 4.788
1.81 5.3757
1.07 2.5252
1.53 3.0906
1.46 4.3362
1.38 3.2016
1.77 4.3542
1.88 4.8692
1.32 3.8676
1.75 3.9375
1.94 5.7424
1.19 2.4752
1.31 26.2
1.56 4.5708
1.16 2.842
1.22 2.44
1.72 5.1256
1.45 4.3355
1.43 4.2471
1.19 3.5343
2 5.46
1.6 3.84
1.58 3.8552
18) Add trendline, regression equation and r squared to the plot.
Add this title. ("Scatterplot of X and Y Data")
19) The scatterplot reveals a point outside the point pattern. Copy the data to a new location in the worksheet. You now have 2 sets of data.
Data that are more tha 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers and must be investigated.
It was determined that the outlying point resulted from data entry e
or. Remove the outlier in the copy of the data.
Make a new scatterplot linked to the cleaned data without the outlier, and add title ("Scatterplot without Outlier,") trendline, and regression equation label.
X Y
1.01 2.8482
1.48 4.2772
1.8 4.788
1.81 5.3757
1.07 2.5252
1.53 3.0906
1.46 4.3362
1.38 3.2016
1.77 4.3542
1.88 4.8692
1.32 3.8676
1.75 3.9375
1.94 5.7424
1.19 2.4752
1.56 4.5708
1.16 2.842
1.22 2.44
1.72 5.1256
1.45 4.3355
1.43 4.2471
1.19 3.5343
2 5.46
1.6 3.84
1.58 3.8552
Compare the regression equations of the two plots. How did removal of the outlier affect the slope and R2? Explain why the slope and R Square change the way they did
20)
HW11
MGMT 650
Fall 21 Week 11 Homework Questions
(Last updated 8/16/2021)
Chi Square
An analyst at a local bank wonders if the age distribution of customers coming for service at his
anch in town is the same as at a
anch located near the mall. He selects 100 transactions at random from each
anch and researches the age information for the associated customer. These are the data :
Age
less than 30 30-55 56 or older Total
In town 20 40 40 100
mall 30 50 20 100
Total 50 90 60 200
1 What is the null hypothesis if you want to check if the age patterns of customers are independent of bank location?
2 What are the expected numbers for each cell in a 3 by 3 table if the null hypothesis is true?
3 Use the chi square test to accept or reject the null hypothesis. What is the chi square test statistic?
4 What is the chi square critical value and how many degrees of freedom does it have? Assume alpha is .05.
5 What do you conclude?
ANOVA
Saeko owns a yarn shop and want to expands her color selection.
Before she expands her colors, she wants to find out if her customers prefer one
and
over another
and. Specifically, she is interested in three different types of bison yarn.
As an experiment, she randomly selected 21 different days and recorded the sales of each
and.
At the .10 significance level, can she conclude that there is a difference in preference between the
ands?
Misa's Bison Yak-et-ty-Yaks Buffalo Yarns
799 776 799
784 640 931
807 822 794
675 856 920
795 616 731
875 893 837
Total 4,735.00 4,603.00 5,012.00
6) What is the null hypothesis?
What is the alternative hypothesis?
What is the level of significance?
7) Use Tools - Data Analysis - ANOVA:Single Factor
to find the F statistic:
8) From the ANOVA output: What is the F value?
What is the F critical value?
9) What is your decision?
Explain in statistical terms
Regression
Studies have shown that the frequency with which shoppers
owse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you
owse online retailers per year?”
Age (X) Time (Y)
16 307
17 285
19 267
22 343
22 393
22 287
22 253
28 364
28 251
28 248
28 433
30 319
33 226
34 321
35 336
35 302
35 476
36 395
39 473
39 342
40 539
42 455
43 326
44 565
48 385
50 590
50 507
51 333
52 426
54 261
58 625
59 252
60 615
10) Use Data > Data Analysis > Co
elation to compute the co
elation checking the Labels checkbox.
11) Use the Excel function =CORREL to compute the co
elation. If answers for #1 and 2 do not agree, there is an e
or.
The strength of the co
elation motivates further examination.
12) a) Insert Scatter (X, Y) plot linked to the data on this sheet with Age on the horizontal (X) axis.
b) Add to your chart: the chart name, vertical axis label, and horizontal axis label.
c) Complete the chart by adding Trendline and checking boxes
Read directly from the chart:
13) a) Intercept =
b) Slope =
c) R2 =
Perform Data > Data Analysis > Regression.
14) Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the R Square in orange
15) Use Excel to predict the number of minutes spent by a 22-year old shopper. Enter = followed by the regression formula.
Enter the intercept and slope into the formula by clicking on the cells in the regression output with the results.
16) Is it appropriate to use this data to predict the amount of time that a 9-year-old will be on the Internet?
If yes, what is the amount of time, if no, why?
Cleaning Data with Outlie
17) On this worksheet, make an XY scatter plot linked to the following data:
X Y
1.01 2.8482
1.48 4.2772
1.8 4.788
1.81 5.3757
1.07 2.5252
1.53 3.0906
1.46 4.3362
1.38 3.2016
1.77 4.3542
1.88 4.8692
1.32 3.8676
1.75 3.9375
1.94 5.7424
1.19 2.4752
1.31 26.2
1.56 4.5708
1.16 2.842
1.22 2.44
1.72 5.1256
1.45 4.3355
1.43 4.2471
1.19 3.5343
2 5.46
1.6 3.84
1.58 3.8552
18) Add trendline, regression equation and r squared to the plot.
Add this title. ("Scatterplot of X and Y Data")
19) The scatterplot reveals a point outside the point pattern. Copy the data to a new location in the worksheet. You now have 2 sets of data.
Data that are more tha 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers and must be investigated.
It was determined that the outlying point resulted from data entry e
or. Remove the outlier in the copy of the data.
Make a new scatterplot linked to the cleaned data without the outlier, and add title ("Scatterplot without Outlier,") trendline, and regression equation label.
X Y
1.01 2.8482
1.48 4.2772
1.8 4.788
1.81 5.3757
1.07 2.5252
1.53 3.0906
1.46 4.3362
1.38 3.2016
1.77 4.3542
1.88 4.8692
1.32 3.8676
1.75 3.9375
1.94 5.7424
1.19 2.4752
1.56 4.5708
1.16 2.842
1.22 2.44
1.72 5.1256
1.45 4.3355
1.43 4.2471
1.19 3.5343
2 5.46
1.6 3.84
1.58 3.8552
Compare the regression equations of the two plots. How did removal of the outlier affect the slope and R2? Explain why the slope and R Square change the way they did
20)