Data Project 1use a significance level of 005 Companies in t

Data Project 1-use a significance level of 0.05

Companies in the Dow Jones Industrial Average

Company

Price

Change

% Change

Volume

YTD
change

MMM 3M

141.26

+0.48

+0.34%

2,506,009

-14.03%

AXP American Express

75.50

+0.19

+0.25%

3,844,194

-18.85%

AAPL Apple

114.21

+1.64

+1.46%

49,915,473

+3.47%

BA Boeing

134.67

+1.12

+0.84%

2,628,223

+3.61%

CAT Caterpillar

72.63

+0.21

+0.29%

4,413,804

-20.65%

CVX Chevron

75.79

+0.13

+0.17%

11,032,075

-32.44%

CSCO Cisco

26.02

-0.24

-0.91%

21,529,112

-6.45%

KO Coca-Cola

38.13

-0.29

-0.75%

11,802,271

-9.69%

DIS Disney

104.48

+1.88

+1.83%

9,529,778

+10.92%

DD E I du Pont de Nemours and Co

48.44

-0.18

-0.37%

6,499,111

-31.04%

XOM Exxon Mobil

72.69

+0.17

+0.23%

12,172,259

-21.37%

GE General Electric

24.95

+0.27

+1.09%

31,903,035

-1.27%

GS Goldman Sachs

185.27

-0.64

-0.34%

2,536,786

-4.42%

HD Home Depot

115.44

+0.95

+0.83%

4,472,836

+9.97%

IBM IBM

147.37

+1.17

+0.80%

3,115,053

-8.15%

INTC Intel

29.47

+0.20

+0.68%

21,786,879

-18.79%

JNJ Johnson & Johnson

92.93

+0.21

+0.23%

7,381,327

-11.13%

JPM JPMorgan Chase

62.56

-0.10

-0.16%

12,766,683

-0.03%

MCD McDonald\'s

97.41

+2.16

+2.27%

6,656,255

+3.96%

MRK Merck

52.09

-0.63

-1.19%

12,090,801

-8.28%

MSFT Microsoft

43.48

+0.19

+0.44%

27,132,527

-6.39%

NKE Nike

111.82

+1.44

+1.30%

2,794,776

+16.30%

PFE Pfizer

32.97

+0.35

+1.07%

22,379,477

+5.84%

PG Procter & Gamble

68.42

+0.10

+0.15%

11,291,401

-24.89%

TRV Travelers Companies Inc

99.49

+0.40

+0.40%

1,375,340

-6.01%

UTX United Technologies

92.33

+0.93

+1.02%

4,490,240

-19.71%

UNH UnitedHealth

118.70

+1.93

+1.65%

3,752,461

+17.42%

VZ Verizon

45.73

+0.27

+0.59%

11,227,446

-2.24%

V Visa

70.76

+0.53

+0.75%

6,452,146

+7.95%

WMT Wal-Mart

64.65

+0.53

+0.83%

8,062,420

-24.72%

Data as of Sep 11

Gain or loss for each stock over the last quarter

Test the claim that the mean is the stocks broke even (no gain or loss indicates a mean of 0)

Company	Price	Change	% Change	Volume	YTD change
MMM 3M	141.26	+0.48	+0.34%	2,506,009	-14.03%
AXP American Express	75.50	+0.19	+0.25%	3,844,194	-18.85%
AAPL Apple	114.21	+1.64	+1.46%	49,915,473	+3.47%
BA Boeing	134.67	+1.12	+0.84%	2,628,223	+3.61%
CAT Caterpillar	72.63	+0.21	+0.29%	4,413,804	-20.65%
CVX Chevron	75.79	+0.13	+0.17%	11,032,075	-32.44%
CSCO Cisco	26.02	-0.24	-0.91%	21,529,112	-6.45%
KO Coca-Cola	38.13	-0.29	-0.75%	11,802,271	-9.69%
DIS Disney	104.48	+1.88	+1.83%	9,529,778	+10.92%
DD E I du Pont de Nemours and Co	48.44	-0.18	-0.37%	6,499,111	-31.04%
XOM Exxon Mobil	72.69	+0.17	+0.23%	12,172,259	-21.37%
GE General Electric	24.95	+0.27	+1.09%	31,903,035	-1.27%
GS Goldman Sachs	185.27	-0.64	-0.34%	2,536,786	-4.42%
HD Home Depot	115.44	+0.95	+0.83%	4,472,836	+9.97%
IBM IBM	147.37	+1.17	+0.80%	3,115,053	-8.15%
INTC Intel	29.47	+0.20	+0.68%	21,786,879	-18.79%
JNJ Johnson & Johnson	92.93	+0.21	+0.23%	7,381,327	-11.13%
JPM JPMorgan Chase	62.56	-0.10	-0.16%	12,766,683	-0.03%
MCD McDonald\'s	97.41	+2.16	+2.27%	6,656,255	+3.96%
MRK Merck	52.09	-0.63	-1.19%	12,090,801	-8.28%
MSFT Microsoft	43.48	+0.19	+0.44%	27,132,527	-6.39%
NKE Nike	111.82	+1.44	+1.30%	2,794,776	+16.30%
PFE Pfizer	32.97	+0.35	+1.07%	22,379,477	+5.84%
PG Procter & Gamble	68.42	+0.10	+0.15%	11,291,401	-24.89%
TRV Travelers Companies Inc	99.49	+0.40	+0.40%	1,375,340	-6.01%
UTX United Technologies	92.33	+0.93	+1.02%	4,490,240	-19.71%
UNH UnitedHealth	118.70	+1.93	+1.65%	3,752,461	+17.42%
VZ Verizon	45.73	+0.27	+0.59%	11,227,446	-2.24%
V Visa	70.76	+0.53	+0.75%	6,452,146	+7.95%
WMT Wal-Mart	64.65	+0.53	+0.83%	8,062,420	-24.72%

Solution

Here we have given the data of companies in the Dow Jones Industrial Average.Gain or loss for each stock over the last quarter.

We have to test the claim that, the mean is the stocks broke even.

Hypothesis for test is,

H₀ : µ = 0 vs H₁ : µ 0

This we can done by using EXCEL.

Here we use x variable as Company Price.

This is the data which have to test the hypothesis .

Here data is given to us population standard deviation is unknown and sample size n 30 so we use here one sample t-test.

The t-statistic value for testing hypothesis is,

t = ( xbar - µ ) / (s/sqrt(n)) (sqrt(n) means square root of n)

This statistic follows t - distribution with n-1 degrees of freedom.

Where, xbar = sample mean.

n = sample size = 30

µ = Population mean

s = sample standard deviation

s / sqrt(n) = standard error or se

The EXCEL command for this testing is,

Enter the data in excel sheet

count(range of x) =This command will gives us number of observations in the sample.

average(range of x) = This command will gives us sample mean xbar.

stdev( range of x) = This command will gives us standard deviation of x.

standard error = stdev(range of x) / count(range of x)

hypothesis mean = 0

= 0.05 = level of significance.

tails = 2

degrees of freedom (d.f.) = n-1 =30-1 = 29

calculate t-statistics.

p-value = tdist(x, d.f. , tails) here x is the t-statistic value.

tinv(probability,d.f.) This will gives us critical value.

If we apply all these commands then we get the following output.

Here from this table ,

tstatistic = 11.222

tcritical = 2.045

p-value = 4.5257 * 10^-12  = 0.0000

tstatistic > tcritical

Reject H₀ at 5 % level of significance.

From p-value we can also conclude that H₀ is rejected.

If p-value < (0.05)

then we reject H₀ at 5% level of significance.

It means mean is differ from 0.

no	x
1	141.26
2	75.5
3	114.21
4	134.67
5	72.63
6	75.79
7	26.02
8	38.13
9	104.48
10	48.44
11	72.69
12	24.95
13	185.27
14	115.44
15	147.37
16	29.47
17	92.93
18	62.56
19	97.41
20	52.09
21	43.48
22	111.82
23	32.97
24	68.42
25	99.49
26	92.33
27	118.7
28	45.73
29	70.76
30	64.65