Overview

HW11 Chi Square ANOVA Regression Cleaning Data with Outlier

Sheet 1: HW11

Sheet 2: Chi Square

	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
		less than 30	30-55	56 or older	Total
	In town	25	37	38	100
	mall	30	48	22	100
	Total	55	85	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?
			Age
		less than 30	30-55	56 or older	Total
	In town				0
	mall				0
	Total	0	0	0	0
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?

Sheet 3: 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 .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
		873	822	794
		702	812	920
		795	673	731
		875	893	837
	Total	4,828.00	4,616.00	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

Sheet 4: 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 year?"
	Note that this sheet includes questions 10-16
	Age (X)	Time (Y)
	16	420
	17	269
	19	315
	22	337
	22	243
	22	459
	22	414
	28	224
	28	381
	28	412
	28	576
	30	333
	33	551
	34	548
	35	626
	35	521
	35	562
	36	699
	39	643
	39	455
	40	666
	42	553
	43	459
	44	525
	48	559
	50	507
	50	612
	51	710
	52	378
	54	566
	58	652
	59	725
	60	695
10)	Use Data > Data Analysis > Correlation to compute the correlation checking the Labels checkbox.
11)	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.
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 an 85-year-old will spend browsing online retailers ?
	If yes, what is the amount of time, if no, why?

Sheet 5: Cleaning Data with Outlier

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 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
20)