stat analysis homework and excel lab

Question 1 Prob 10-22

Tutorial

EXCEL INSTRUCTIONS:

JMP INSTRUCTIONS:

DS 123 Lab #4

1. Under File, select Page Setup. Select the top tab: Sheet.

To add the JMP output for Problem 10.22:

In the Print window, select Gridlines and Row and Column Headers.

a.      Open JMP.

2. Set column A to width 10 and column C to 16.

b.      File – New – Data Table.

3. Insert a page break above row 46.

c.       Column 1 enter Miller's in cells 1 – 10, Albert's in cells 11 - 20.

d.      Rename column 1 Markets.

Question 1.

Problem 10.10, pp. 389 - 390

e.       Go back to this Excel spreadsheet. Copy Miller's values from Excel. On JMP table, double click on column 2 cell 1, Control-V to paste the ten values.

Miller's

t-Test: Two-Sample Assuming Equal Variances

f.       Go back to this Excel spreadsheet. Copy Albert's values from Excel. On JMP table, paste the values in column 2 cells 11-20.

$119.25

Go to the Data ribbon and select Data Analysis.

g.      Rename column Grocery Expenses.

$121.32

Miller's

Albert's

Select t-Test: Two-Sample Assuming Equal Variances

h.      Highlight Grocery Expenses title, select Col-Column info. In the window, format – Dec should show 2, not 0. Click OK.

$122.34

Mean

121.916

114.807

Select the data streams for each variable, including their labels.

i.        Analyze-Fit Y by X.

$120.14

Variance

1.9550044444

3.3867122222

Change the alpha level to .01

j.        Move Grocery Expenses to Y, Response. Move Markets to X, Factor. Click OK.

$122.19

Observations

10

10

Mark that labels were included.

k.      Click the red diamond next to Oneway Analysis.

$123.71

Pooled Variance

2.6708583333

Place the output in cell C8.

Select Means/Anova/Pooled t.

$121.72

Hypothesized Mean Difference

0

It will prompt you that you are overwriting

l.        ALT-Edit-Copy.

$122.42

df

18

material. Click 'Ok'.

m.    Go back to this Excel spreadsheet. In cell M23, paste the JMP report.

$123.63

t Stat

9.7267575315

n.      From the JMP report, right click on the Oneway Analysis graphic. Edit-Copy graph.

$122.44

P(T<=t) one-tail

0.0000000068

o.      On this Excel spreadsheet, paste the graph with the upper left corner located on P27.

t Critical one-tail

2.5523786462

p.      From the JMP report, right click on the t-Test assuming equal variances graphic. Edit – Copy graph.

Albert's

P(T<=t) two-tail

0.0000000137

q.      On this Excel spreadsheet, paste the graph with the upper left corner located on cell R48.

$111.99

t Critical two-tail

2.8784415917

$114.88

JMP OUTPUT

$115.11

t-Statistic

p-value

$117.02

$116.89

Hypotheses:

Oneway Analysis of Grocery Expenses By Markets

$116.62

$115.38

$114.40

Rejection Region:

a = 0.01

a = 0.01

$113.91

df = 18

Rej H0 if p-value < 0.01

$111.87

t-coeff =

2.8784404727

Oneway Anova

Rej H0 if t > 2.878 or

t < - 2.878

Test Statistic:

t =

9.7267575315

p-value =

0.0000000137

Summary of Fit

Conclusion:

Since the test statistic of t = 9.727 falls

Since the test statistic of

Rsquare

0.840156

WAY above the upper critical value

p-value = 1.37 x 10^-8 falls below

Adj Rsquare

0.831276

of t = 2.878, we reject H0

alpha=0.01,we reject

Root Mean Square Error

1.634276

with at least 99% confidence.

H0 with at least 99% confidence.

Mean of Response

118.3615

Implication:

Observations (or Sum Wgts)

20

There is enough evidence to

There is enough evidence to

conclude that the mean weekly expenses

conclude that the mean weekly

at Miller's and Albert's differ.

expenses at Miller's and Albert's

differ.

t Test

Miller's-Albert's

Assuming equal variances

Difference

7.109

t Ratio

9.726758

Std Err Dif

0.73087

DF

18

Upper CL Dif

8.6445

Prob > |t|

<.0001

Lower CL Dif

5.5735

Prob > t

<.0001

Confidence

0.95

Prob < t

1

Analysis of Variance

Source

DF

Sum of Squares

Mean Square

F Ratio

Prob > F

Markets

1

252.6894

252.689

94.6098

<.0001

Error

18

48.07545

2.671

C. Total

19

300.76485

Means for Oneway Anova

Level

Number

Mean

Std Error

Lower 95%

Upper 95%

Albert's

10

114.807

0.5168

113.72

115.89

Miller's

10

121.916

0.5168

120.83

123

Std Error uses a pooled estimate of error variance

Question 2

															JMP INSTRUCTIONS
Question 2.	Problem Given on Assignment														To add the JMP output for question 2:
Branch A		F-Test Two-Sample for Variances				Go to the Data ribbon and select Data Analysis.									a.      Open JMP.
$307,000						Select F-Test Two-Sample for Variances									b.      File – New – Data Table.
$316,000			Branch A	Branch B		Select the data streams for each variable, including their labels.									c.       Column 1 enter Branch A in cells 1 – 14, Branch B in cells 15 – 30.
$307,000		Mean	301500	290312.5		Mark that labels were included.									d.      Rename column 1 Branches
$305,000		Variance	269653846.153846	97562500		Change the alpha level to 0.10 -- so the one-tailed critical bound will be at 0.05.									e.       Go back to this Excel spreadsheet. Copy Branch A loan values from Excel. On JMP table, double click on column 2 cell 1, Control-V to paste the fourteenvalues.
$294,000		Observations	14	16		Place the output in cell C47.									f.       Go back to this Excel spreadsheet. Copy Branch B loan values from Excel. On JMP table, paste the values in column 2 cells 15 – 30.
$303,000		df	13	15			It will prompt you that you are overwriting								g.      Rename column Loans.
$297,000		F	2.763908737				material. Click 'Ok'.								h.      Analyze-Fit Y by X.
$286,000		P(F<=f) one-tail	0.0314249074			Notice: you will REJECT H0. There IS enough evidence to say the variances are different!									i.        Move Loans to Y, Response. Move Branches to X, Factor. Click OK.
$265,000		F Critical one-tail	2.0001493795												j.        Click the red diamond next to Oneway Analysis.
$320,000															Select t-Test.
$315,000		t-Test: Two-Sample Assuming Unequal Variances													k.      ALT-Edit-Copy.
$328,000						Go to the Data ribbon and select Data Analysis.									l.        Go back to this Excel spreadsheet. In cell P20, paste the JMP report.
$285,000			Branch A	Branch B		Since you rejected H0 on the F-test above, you will									m.    From the JMP report, right click on the t-Test assuming unequal variances graphic. Edit – Copy graph.
$293,000		Mean	301500	290312.5		select t-Test: Two-Sample Assuming Unequal Variances									n.      On this Excel spreadsheet, paste the graph with the upper left corner located on cell U27.
		Variance	269653846.153846	97562500		Select the data streams for each variable, including their labels.
Branch B		Observations	14	16		Mark that labels were included.									JMP OUTPUT
$304,000		Hypothesized Mean Difference	0			Place the output in cell C58.
$289,000		df	21				It will prompt you that you are overwriting
$296,000		t Stat	2.2216212668				material. Click 'Ok'.								Oneway Analysis of Loans By Branches
$283,000		P(T<=t) one-tail	0.0187168709			Notice: the df is NOT equal to n1 + n2 - 2.
$281,000		t Critical one-tail	1.7207435121
$301,000		P(T<=t) two-tail	0.0374337418
$298,000		t Critical two-tail	2.0796142053
$303,000															t Test
$301,000			t-Statistic		p-value										Branch B-Branch A
$288,000
$298,000		Hypotheses:													Assuming unequal variances
$286,000
$284,000
$283,000		Rejection Region:	a = 0.05		a = 0.05
$277,000			df = 21		Rej H0 if p-value < 0.05										Difference	-11188	t Ratio	-2.22162
$273,000			t-coeff =	2.0796138447											Std Err Dif	5036	DF	20.73312
			Rej H0 if t < -2.08 or												Upper CL Dif	-707	Prob > |t|	0.0376
			t > 2.08												Lower CL Dif	-21668	Prob > t	0.9812
		Test Statistic:	t =	2.2216212668	p-value =	0.0374337432									Confidence	0.95	Prob < t	0.0188
		Conclusion:
		Since the test statistic of t = 2.222 falls			Since the test statistic of
		abovethe upper critical			p-value = .037 falls below
		value of t = 2.080, we reject			a = 0.05, we reject										Tests that the Variances are Equal
		H0 with at least 95% confidence.			H0 with at least 95% confidence.
		Implication:
		There is enough evidence to			There is enough evidence to										Level	Count	Std Dev	MeanAbsDif to Mean	MeanAbsDif to Median
		conclude that the average weekly			to conclude that the average										Branch A	14	16421.14	12714.29	12500
		expenses differs for the two stores.			weekly expenses differ										Branch B	16	9877.37	8601.56	8437.5
					for the two stores.
															Test	F Ratio	DFNum	DFDen	p-Value
															O'Brien[.5]	2.7	1	28	0.1115
															Brown-Forsythe	1.9358	1	28	0.1751
															Levene	2.3234	1	28	0.1387
															Bartlett	3.4123	1	.	0.0647
															F Test 2-sided	2.7639	13	15	0.0628
															Welch's Test
															Welch Anova testing Means Equal, allowing Std Devs Not Equal
															F Ratio	DFNum	DFDen	Prob > F
															4.9356	1	20.733	0.0376
															t Test
															2.2216

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