Chat with us, powered by LiveChat 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. - Essayabode

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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