An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at a branch located near the mall.
An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at a branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer. These are the data :
Age
Expected
Chi-square
less than 30
30-55
56 or older
Total
less than 30
30-55
56 or older
Total
less than 30
30-55
56 or older
In town
20
40
40
100
In town
25
45
30
100
In town
1
0.555556
3.333333
mall
30
50
20
100
mall
25
45
30
100
mall
1
0.555556
3.333333
Total
50
90
60
200
Total
50
90
60
200
X2
9.777778
Df
2
What is the null hypothesis if you want to check if the age patterns of customers are independent of bank location?
What are the expected numbers for each cell in a 3 by 3 table if the null hypothesis is true?
Use the chi square test to accept or reject the null hypothesis. What is the chi square test statistic?
What is the chi square critical value and how many degrees of freedom does it have? Assume alpha is .05.
What do you conclude?
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 brand
over another brand. 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 brand.
At the .10 significance level, can she conclude that there is a difference in preference between the brands?
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
What is the null hypothesis?
What is the alternative hypothesis?
What is the level of significance?
Use Tools – Data Analysis – ANOVA:Single Factor
to find the F statistic:
Anova: Single Factor
From the ANOVA output: What is the F value?
What is the F critical value?
What is your decision?
Explain in statistical terms
Studies have shown that the frequency with which shoppers browse 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 browse 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
Use Data > Data Analysis > Correlation to compute the correlation checking the Labels checkbox.
Use the Excel function =CORREL to compute the correlation. If answers for #1 and 2 do not agree, there is an error.
The strength of the correlation motivates further examination.
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:
a) Intercept =
b) Slope =
c) R2 =
Perform Data > Data Analysis > Regression.
Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the R Square in orange
SUMMARY OUTPUT
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.
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?
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
Add trendline, regression equation and r squared to the plot.
Add this title. (“Scatterplot of X and Y Data”)
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 error. 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
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