Reference no: EM132343751

Chi Square

Saeko has a yarn shop and wants to test her theory on what types of colors she is selling.

She believes that Black, White, the Primary Colors, and Tertiary colors sell in equal amounts.

Test Saeko's theory using the 5 step hypothesis testing analysis and Chi Square at the .10 level of significance.

(optional) Use the "Pivot Table Data" tab to create a pivot table that shows Saeko the number of yards that were sold in the various yarn types during the busiest weekend of her shop last year.

The pivot table should contain Color Type, Sum of Yards and Count of Color Type as Column Titles.

Here is the pivot table that you should have created. It is optional so that you can practice your pivot table skills.

Color Type	Sum of Yards	Count of Color Type
Black	19,762.00	23
Blue	8,127.00	20
Brown	8,027.00	13
Green	6,533.00	12
Purple	7,243.00	12
Red	5,194.00	10
White	17,649.00	26
Yellow	7,229.00	14
Grand Total	79,764.00	130

1) Using the pivot table that you just created, fill in the blanks in the following table:
Primary Colors consists of the sum of Blue, Red, and Yellow yarn sold
Tertiary Colors consists of the sum of Brown, Green, and Purple Colors Sold.
The Total in this chart must equal the Grand Total, Cell D16 in the above table.

Color Type	Sum of Yards
Black
White
Primary Colors
Tertiary Colors
Total

This table represents the observed data in the Chi Square analysis.

Find the Expected values for each of the colors. Saeko expects that the colors sell in equal amounts.

2) Use the 5 step hypothesis testing procedure to determine if Saeko's hypothesis that the colors sell in equal amounts is true.
What is the null hypothesis?
What is the alternative hypothesis?

What is the level of significance?

What is the Chi Square test statistic?

3) What is the Chi Square critical Value?

4) What is your answer to Saeko?

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 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 .01 significance level, can she conclude that there is a difference in preference between the brands?

	Misa's Bison	Yak-et-ty-Yaks	Buffalo Yarns
	343	365	360
	308	368	346
	349	351	381
	304	339	306
	348	366	314
	346	331	307
Total	1,998.00	2,120.00	2,014.00

5) What is the null hypothesis?
What is the alternative hypothesis?

What is the level of significance?

6) Use Tools - Data Analysis - ANOVA:Single Factor
to find the F statistic:

7) From the ANOVA ooutput: What is the F value?

8) What is the F critical value?

9) What is your decision?

Regression

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 week?"

Age (X)	Time (Y)
13	5662
19	4549
16	3772
44	1872
32	2799
52	1355
39	1966
15	5682
40	1602
53	1186
48	1832
37	2253
36	2241
42	1001
30	2474
42	1943
28	3021
11	5682
32	2192
39	1784
23	2707
37	1801
17	4827
11	2693
18	4340
50	1399
52	1593
9	9154
41	1504
26	2627
30	2575
32	2711
53	2368

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:
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 total standard error in orange
SUMMARY OUTPUT

Use Excel to predict the number of minutes spent by a 37-year old shopper. Enter = followed by the regression formula.

15) 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 68-year-old will be on the Internet?

If yes, what is the amount of time, if no, why?

17) On this worksheet, make an XY scatter plot linked to the following data:

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 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.

20. Compare the regression equations of the two plots. How did removal of the outlier affect the slope and R²?

Attachment:- Statistics for Managerial Decision Making.rar