>Output

Hypothesis

Test: Mea

nvs.

HypothesizedValue

1,

1 5 0.000 hypothesized value 1,1

8 3.

235 mean Score 11

8.

9 79 std. dev. 20

.

405 std. error 34

n

33
df
1.

3 t .05

64 p-value(one-tailed, upper) Hypothesis Test:

Meanvs. Hypothesized Value

1,

15 0.000hypothesized value

1,1 83.2

35 mean Score 1 18.

979

std. dev.

20. 405

std. error

34 n

33 df

1.

t

.0

4

p-value (one-tailed, upper) Hypothesis Test: Mean vs. Hypothesized Value 1,1 50.000

hypothesized value

1,183.235 mean Score

.9

79 std. dev.

20.405 std. error

34 n

p-value (one-tailed, upper)

Hypothesis Test: Independent Groups (t-test,

) On-campus Commuter 87

.

13 76.

93 mean

8.64
9.

std. dev.

15 15 n

28

df

10

.

200 dif ference (On-campus – Commuter) 82

.

810

pooled variance

9.

3 standard error of

difference 0 hypothesized difference 3.07

t

.00

.15

777777777

78 82.83 12 5. 964 No

rth 73.1

577777777778 72

.

8010

10.0 43 South 73.1577777777778 73.1311

8. 205 Central 73.1577777777778 63.8 112

5.820 East 73. 16 45 10.134 Total ANOVA table Source SS df MS F p-value Treatment 2,173.6323

7 24.5

440 12.

67 5.34E-06 Error 2,344.778 41 57.1 897 Total

4, 518.410

44

Post hoc analysis
p-values

r pairwise t-tests East South Central

North 63.81 72.80 73.13 82.83

East 63.81

South 72.80

16 North 82.83

2.54E-07 .0035 .00 37 Tukey simultaneous comparison t-values (d.f. = 41) East South Central North

63.81 72.80 73.13 82.83

East 63.81

3.32

Goodness of Fit Test
observed
expected
O – E
(O – E)² / E
% of chisq
200

3.000 7.0

00 0.

254 6.

94 200 20 2.000 -2.000 0.020 0.54 200

1 84.000 1

6.000 1.3

91 38.01 200

22 1.000 –

21.000 1.

995 54.51 800 800.000

0.000

3. 660
100.00
3.66
chi-square
3 df

.

05

p-value

Chi-square Contingency Table Test for Independence
UG
GR
totals
Total
Y

es Observed 49 47 96 192 Expected 63.

61 32. 39 96.00 192.00 No Observed 1 14 36 150 300 Expected 99.39 50.61 150.00 300.00 totals Observed 163 83 2 46 492 Expected 163.00 83.00 246.00 492.00 Total Observed

3 26 166492

984 Expected

326.00 166.00492.00

98 4.00 16.

31 chi-square

4 df

.0026

p-value

Correlation Matrix
Aptitude
Sales
Aptitude

73019

904

539 Sales

.822 1.000

19

Analysis r² 0.675 n 19 r 0.822 k

1

Std. Error
28.198
Dep. Var.

Sales

ANOVA table

Source

MS F p-value

Regression

28,138.0066

35.39 1. 59E-05 Residual 13,517.15

13 17 795.12

65 Total 41,6 55.1579 18 Regression output confidence interval variables coefficients std. error t (df=17)

p-value

95% lower 95% upper Intercept 335.9 221 27.3

1 48 12. 298 6.91E-10 278.2928 393.5513 Aptitude

1.4732 0.2477 5.949 1.59E-05 0.9 507 1.9957 Predicted values for: Sales 95% Confidence Interval 95% Prediction Interval Aptitude

Predictedlower

upperlower upper

Leverage 107 493.557 479.908 507.206 432.519 554.595 0.053Hypothesis Test: Mean vs. Hypothesized Value

80.000 hypothesized value

83.528
mean

std. dev.

2.206

std. error

36

n

35

df

1.

t

.0593

p-value (one-tailed, upper)

Hypothesis Test: Independent Groups (t-test, pooled variance)
Briar Hills
Englewood
338.

2 315.264

mean

26.755
31.781

std. dev.

12 14 n

24

df

23.4774
difference (Briar Hills – Englewood)
875.1917

pooled variance

29.

36

pooled std. dev.

11.6381
standard error of difference

0 hypothesized difference

2.02 t

.0275

p-value (one-tailed, upper)

Hypothesis test for proportion vs hypothesized value
Observed Hypothesized

0.73
0.

.0511

p-value (one-tailed, upper)

Hypothesis test for two independent proportions
p1
p2
pc
0.

p (as decimal)

64/

/

283 p (as fraction)

63.99
52.984
116

.974

X

135 148 283 n

0.116

difference

0

std. error

1.98

z

.0478

p-value (two-tailed)

Comparison of Groups

North South Central East 87.0

82.4 60.1 54.2 82.976.0

65.7 70.2

91.1 67.2 62.3 67.4 85.3

74.6 80.4 71.9 79.0

80.5 64.5 59.6 74.4 59.5 75.3 67.8 76.9 84.477.0

54.6 85.6 59.879.0

66.484.0

61.1 79.2 61.4 91.8 82.5 78.861.4

82.6 82.162.3

73.4 68.582.83333333333333 72.8 73.12727272727273 63.80833333333334 73.1577777777778 73.1577777777778 73.1577777777778 73.1577777777778

73.0 7

5.083.0 83.0 85.0 85.0 89.0 93.0 93.0

103.0

105.0 107.0 117.0

120.0

129.0

141.0

147.0

153.0

155.0

462.0

447.0

408.0

435.0

483.0

486.0

465.0

480.0 507.0 474.0

512.0

456.0 468.0

541.0

524.0

522.0

594.0

581.0

537.0

Aptitude

Sales

## Sheet1

to show there are or there are no difference between what you are testing and the current situation.

ly above the university mean of

0. Level of signifance (Alpha) is 95%

Score9

1

4

0

7

7

Hypothesis Test: Mean vs. Hypothesized Value

1,150.000 hypothesized value

1,183.235 mean Score

118.979 std. dev.

20.405 std. error

6

34 n

6

1.63 z

1

.0517 p-value (one-tailed, upper)

5

1247

8

9

On-campus Commuter 86 7179 80

88 83

97 87

88 76

85 62

97 68

79 82

88 84

87 75

91 84

86 61

104 72

67 96

85 73

Hypothesis Test: Independent Groups (t-test, pooled variance)

On-campus Commuter

mean

15 15 n

28 do

difference (On-campus – Commuter)

pooled variance

standard error of difference

3.07 t

.0047 p-value (two-tailed)

1.0 Income 79 95

77

105

65

100

67

95

8376

83

9379

75

79

62103

77

8774

76

10773

89

97

80

64

96

78

76

70 78

65

106

2.0Briar Hills Englewood

277

87 82.4 60.1 54.2

82.9 76 65.7 91.1 67.2 62.3 67.4

74.6 80.4

79 80.5 64.5 59.674.4 59.5 75.3 67.8

76.9 84.4 77 54.6

85.6 59.8 79 66.4

84 61.1 79.2 61.4

91.8 82.5 78.8 61.4

82.6 82.1 62.3

73.4 68.5

One factor ANOVA

Mean n Std. Dev

73.1577777777778 82.83 12

North

73.1577777777778 72.80 10 10.043 South

73.1577777777778 73.13 11 8.205 Central

73.1577777777778 63.81 12 5.820 East

73.16 45 10.134 Total

ANOVA table

Source SS df MS F p-value

5.34E-06

Error 2,344.778 41Total 4,518.410 44

Post hoc analysis

p-values for pairwise t-tests

East South Central North

63.81 72.80 73.13 82.83

East 63.81

Central 73.13

North 82.83 2.54E-07 .0035 .0037

Tukey simultaneous comparison t-values (d.f. = 41)

East South Central North

63.81 72.80 73.13 82.83

East 63.81

South 72.80 2.78

Central 73.13

0.10

North 82.83 6.16 3.10 3.07

critical values for experimentwise error rate:

0.05

0.01 3.32

5.0 Your turn1

5

4

4

1

4

7

4

4

2.5

5 1 2 3 4 5

5

Englewood Briar Hills

11 4

5

1

3

16

4

3

3

20

5

2

2

4

4

5

27

2

29

4

3

4

2

34

2

5

1

38

4

2

2

3

43

4

1

2

47

5

1

1

4

4

1

2

55

2

1

1

1

5

3

2

63 347.4 3

64

2

4

2

4

5

2

5

4

5

2

5

2

2

4

79

5

3

4

2

4

2

.8

1

87

2

89

3

91 350.7 2

92

5

5

4

4

4

5

2

4

1

4

103

3

4

2

.8

4

5

4

1

1

.5

1

2

5

3

5

5

5

119 328.1 3

120

4

2

123

1

5

North 200

202 South 200 East 200

200

observed expected O – E (O – E)² / E % of chisq

200

7.000

200 -2.000 0.020 0.54

16.000

200 1.995 54.51

100.00

3 df

p-value

Yes 49 47 96

totals 163 83 246

Chi-square Contingency Table Test for Independence

Total

47 96 192

96.00 192.00

36

300

totals Observed

83

492

492.00

166 492

Expected 326.00 166.00 492.00 chi-square

.0026 p-value

6.0 Your turn

Yes 24 50 105

No 49 58 100 20773 108 205 386

Example

. Make predictions for X = 107

X Y X YAptitude Sales Aptitude Sales

73 462 73 462

75 447 75 447

83 408 83 408

83 435 83 435

85 483 85 483

85 486 85 486

89 465 89 465

93 480 93 480

93 507 93 507

103 474 103 474

105 512 105 512

107 456 107 456

117 468 117 468

120 541 120 541

129 524 129 524

141 522 141 522

147 594 147 594

153 581 153 581

155 537 155 537

Correlation Matrix

Aptitude Sales

Aptitude 1.000 Sales .822 1.000

19 sample size

critical value .05 (two-tail)

critical value .01 (two-tail)

Regression Analysis

r² 0.675 n 19

r 0.822 k 1

Std. Error 28.198 Dep. Var. Sales

ANOVA table

Source SS df MS F p-value

Regression

1 28,138.01 35.39 1.59E-05

18

variables coefficients std. error t (df=17) p-value

95% upper

6.91E-10 278.2928 393.5513

95% Confidence Interval 95% Prediction Interval

Aptitude Predicted lower upper lower upper Leverage

493.557 479.908 507.206 432.519 554.595 0.053

X Y

Calls Sales6 19

12 38

14 34

10 24

20 47

22 38

25 60

27 53

29 70

51 46

33 59

36 63

37 70

42 67

44 53

48 57

52 33

Week 4 – More Hypothesizing and some real practical material | ||||

Hypothesis testing is what you | do | |||

The steps we use in this course are: | ||||

Know the Ho (Null Hypothesis or current situation) | ||||

Know the Alpha value | ||||

Enter into MegaStat the H1 (Research Hypothesis) | ||||

Enter the data. | ||||

Make a decision on the Ho, based on the result of the “p-value” computation of H1 | ||||

First we do the Ho testing using the Z or “t” for one or two groups | ||||

Example | An instructor wants to know if the mean entrance exam score of his class of 34 students . | |||

is significant | 115 | |||

1295 | ||||

112 | ||||

1326 | ||||

102 | ||||

1006 | ||||

1206 | ||||

1279 | ||||

123 | ||||

122 | ||||

1301 | ||||

124 | ||||

987 | ||||

104 | ||||

1177 | Note: since the N > 30 one uses the Z test | |||

1040 | ||||

1266 | ||||

1345 | ||||

1230 | ||||

1239 | ||||

1434 | ||||

1385 | ||||

114 | ||||

101 | ||||

1182 | ||||

1012 | ||||

121 | ||||

113 | ||||

1120 | Decision – since p-value > Alpha fail to reject Ho | |||

1 | 277 | Mean score is not statically significant above 1150 | ||

992 | ||||

119 | ||||

1181 | ||||

109 | ||||

Another | example | An instructor wants to know did his On-campus students scored | ||

differently than his On-line students. Alpha = .075 | ||||

87.13 | 76.93 | |||

10.200 | ||||

82.810 | ||||

3.323 | ||||

Decision: since the p-value < Alpha one rejects the Ho and | ||||

can say there is a difference. Note since one did not test | ||||

for greater or less, one can not say which scored higher | ||||

based upon this test | ||||

Your turn | A shopping center developer wants to create a development in a particular area only and only | |||

if the mean income of the homes in the immediate vicinity is greater 80 thousand dollars. Alpha = .025. | ||||

Does the developer build in this area? | ||||

106 | ||||

A developer wants to build a shopping center near Briar Hills, IF the homes there are more expensive | ||||

that the homes in Englewood. Test using Alpha = .05. | ||||

328.1 | 330.9 | |||

368.6 | 350.7 | |||

306.8 | 300.2 | |||

348 | 297.7 | |||

399 | 353.3 | |||

338.6 | 283.2 | |||

337.3 | 271.6 | |||

349.6 | 353.7 | |||

314.4 | ||||

307.4 | 275.8 | |||

347.4 | 343 | |||

319.7 | 339.3 | |||

298.1 | ||||

339.2 | ||||

FYI – you conduct similar test on Proportions | ||||

A professional basketball player has a 62% free throw percentage. Since making a change in his technique | ||||

he has hit 73% out of 52 free throws. Is this evidence that his change has helped? Alpha = .05 | ||||

47.4% of 135 men say they would purchase a particular product, 35.8% of 148 women say they | ||||

would purchase the product. Are these percentages different? | ||||

Do the appropriate test. Alpha =.05 | ||||

Now we statistical test when there are more than two groups (ANOVA test) | ||||

there are several different ANOVA one can use, The version one uses depends upon the groups being tested. In this class we do a simple straight forward test of the means | ||||

Given the sales in the three regions shown below. Test if there are difference in the average sales by region | ||||

70.2 | ||||

85.3 | 71.9 | |||

5.964 | ||||

724.5440 | 12.67 | p-value 9 < .05 so reject Ho | ||

57.1897 | There is a difference in means | |||

FYI – these p-values show which groups are different | ||||

.0052 | .9216 | 2.95 | 2.68 | |

Click in cell A1 to return to the Index. | ||||

No. | Price | SubDiv | ||

480.1 | ||||

397.8 | ||||

413.0 | ||||

389.3 | ||||

331.0 | ||||

381.2 | ||||

42 | ||||

427.3 | Burbsville | Lone Tree | Stanton | |

380.6 | ||||

439.6 | ||||

249.8 | ||||

248.0 | ||||

376.5 | ||||

320.4 | ||||

341.8 | ||||

455.9 | ||||

273.7 | ||||

283.8 | ||||

381.4 | ||||

382.8 | ||||

419.6 | ||||

336.8 | ||||

391.4 | ||||

387.0 | ||||

412.9 | ||||

290.7 | ||||

343.0 | ||||

452.2 | ||||

224.7 | ||||

407.4 | ||||

278.0 | ||||

350.6 | ||||

328.4 | ||||

401.8 | ||||

235.0 | ||||

357.9 | ||||

475.7 | ||||

257.7 | ||||

283.0 | ||||

399.2 | ||||

245.0 | ||||

192.9 | ||||

258.4 | ||||

298.3 | ||||

227.0 | ||||

224.1 | ||||

262.0 | ||||

433.8 | ||||

333.3 | ||||

346.2 | ||||

299.7 | ||||

407.0 | ||||

272.3 | ||||

380.9 | ||||

414.9 | ||||

69 | 354.6 | |||

415.1 | ||||

381.6 | ||||

452.3 | ||||

296.7 | ||||

451.4 | ||||

280.1 | ||||

248.2 | ||||

411.4 | ||||

500.0 | ||||

316.8 | ||||

406.8 | ||||

267.7 | ||||

247.5 | ||||

345.5 | ||||

207 | ||||

276.5 | ||||

309.7 | ||||

511.0 | ||||

460.2 | ||||

411.7 | ||||

383.3 | ||||

392.3 | ||||

450.9 | ||||

341.6 | ||||

379.1 | ||||

197.8 | ||||

390.3 | ||||

296.2 | ||||

390.2 | ||||

348.8 | ||||

386 | ||||

475.5 | ||||

108 | 385.3 | |||

263.6 | ||||

110 | 200.5 | |||

111 | 202 | |||

341.4 | ||||

452.4 | ||||

332.0 | ||||

430.8 | ||||

421.6 | ||||

429.5 | ||||

405.6 | ||||

277.0 | ||||

239.9 | ||||

457.3 | ||||

Now a statistical used with Nominal Data (means are not involved) Chi-Square Test | ||||

Given the sample of units sold in four regions, are the number of units sold in the four regions uniformly distributed? | ||||

test with Alpha = .05 | ||||

193 | note the fo gives the actual data | |||

while the fe gives the expected values if there were an = distribution | ||||

184 | ||||

West | ||||

193.000 | 0.254 | 6.94 | ||

202.000 | ||||

184.000 | 1.391 | 38.01 | ||

221.000 | -21.000 | |||

3.660 | ||||

.3005 | ||||

decision: since p-value > .05 fail to reject. | ||||

the units are evenly distributed. | ||||

another example | This table shows the computer ownership of a sample of GRaduate and UnderGraduate students. | |||

Are the factors independent? Calculate the expected frequencies and perform a chi-square test: Alpha = .05 | ||||

observed frequencies | ||||

Own PC | ||||

UG | GR | totals | ||

49 | ||||

63.61 | 32.39 | |||

114 | 150 | |||

163 | 246 | |||

246.00 | ||||

326 | 984 | |||

984.00 | ||||

16.31 | ||||

decision; Since p-value < Alpha of .05 reject Ho, there is a difference | ||||

This table is a result of a sample of 386 managers from small, medium, and large companies | ||||

who were asked by a local university if they planned to pursue an MBA degree in the next five years. | ||||

Test to see if there are differences – Alpha =.025 | ||||

Size of company | ||||

Small | Medium | Large | ||

Plan MBA? | 179 | |||

Now we move on to Regression, scatter plot and correlation – they are all tied together | ||||

We previously made some scatter plots. Now we move forward and show how it is related to Correlation and | ||||

regression | ||||

These data show the relationship between a sales aptitude test (X) and Sales in thousands (Y). | ||||

A. Use MegaStat to do a | Regression Analysis | |||

Note – the in depended variable is on horizontal axis | ||||

0.8218873019904539 | ||||

± .456 | ||||

± .575 | ||||

Note the r > than the critical values so it | ||||

Also note .822^2 = | 0.675684 | |||

Which is R | ||||

R is the correlation squared and is the relationship (%) between variable | ||||

Now regression – note where we typed the 107 | ||||

28,138.01 | ||||

795.1265 | ||||

41,655.16 | ||||

95% lower | ||||

335.9221 | 27.3148 | 12.298 | ||

0.9507 | 1.9957 | |||

107 | ||||

Use the following data to compute a (1) Scatter plot, (2) a Correlation – state if r is statistical significant, | ||||

(3) state the relationship between the variable in percent, and (4) forecast/predict the sales of sales | ||||

person that makes 22 | Calls | |||

&P of &N

Comparison of Groups

North South Central East 87.0 82.4 60.1 54.2 82.9 76.0 65.7 70.2 91.1 67.2 62.3 67.4 85.3 74.6 80.4 71.9 79.0 80.5 64.5 59.6 74.4 59.5 75.3 67.8 76.9 84.4 77.0 54.6 85.6 59.8 79.0 66.4 84.0 61.1 79.2 61.4 91.8 82.5 78.8 61.4 82.6 82.1 62.3 73.4 68.5 82.83333333333333 72.8 73.12727272727273 63.80833333333334 73.1577777777778 73.1577777777778 73.1577777777778 73.1577777777778

73.0 75.0 83.0 83.0 85.0 85.0 89.0 93.0 93.0 103.0 105.0 107.0 117.0 120.0 129.0 141.0 147.0 153.0 155.0 462.0 447.0 408.0 435.0 483.0 486.0 465.0 480.0 507.0 474.0 512.0 456.0 468.0 541.0 524.0 522.0 594.0 581.0 537.0 Aptitude

Sales

Given the sample of prices, are the prices different in the different subdivisions of the RealEstateData? Sort on subdivsion and form the groups below. Do the analysis with MegaStat.