MGMT650 Homework 11 Latest 2021 July

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