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ADM 2304 E - Statistical Methods Assignment #1

Problem 1

a)

Test and CI for Two Proportions: bmi_A, bmi_B

Null Hypothesis: No significant difference

Alternative Hypothesis: Significant difference

Event = 1

Variable X N Sample p

bmi_A 192 1342 0.143070

bmi_B 97 720 0.134722

Difference = p (bmi_A) - p (bmi_B)

Estimate for difference = 0.143070 Ð'- 0.134722 => 0.00834782

90% CI for difference = (-0.0178288, 0.0345244)

Test for difference = 0 (vs not = 0) Z = 0.52 P-Value = 0.600

Therefore, based on these results we would not reject the null hypothesis. There is no significant difference in the weights of both cities.

Manual

Pooled P-hat = (192 + 97) / (1342 + 720)

= 289 / 2062

= 0.140155

Z-stat = (0.143070 Ð'- 0.134722) Ð'- 0 / sqrt[(0.140155) x (1-0.140155) x (1/1342) x(1/720)]

= 0.008348 / 0.016037

= 0.520546

b)

Confidence Interval = (p1 Ð'- p2) +/- ZÐ"ÐŽ/2 * [sqrt ((p1(1-p1)/n1) + p2(1-p2)/n2)]

= (0.143070 Ð'- 0.134722) +/- 1.645 * [sqrt(0.14307(1-0.14307)/1342) + 0.134722(1-0.134722)/720)

= 0.008348 +/- 0.026179

Therefore this equals the interval of

(-0.0178288, 0.0345244)

The confidence interval calculated above is consistent with the conclusion in question A.

Problem 2

a)

Test and CI for One Proportion: C3

Test of p = 0.5 vs p not = 0.5

Event = 1

Variable X N Sample p 95% CI Exact P-Value

C3 1247 1937 0.643779 (0.621990, 0.665132) 0.000

b & c)

Test and CI for One Proportion: C4, C5, C6, C7, C8, C9, C10, C11, ...

Test of p = 0.5 vs p not = 0.5

Event = 1

Variable X

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23 N

8

16

13

17

10

13

12

14

14

13

15

16

12

16

15

18

18

14

15

14 Sample p

23

23

23

23

23

23

23

23

23

23

23

23

23

23

23

23

23

23

23

23 90% CI

(0.184473, 0.511179)

(0.537839, 0.853466)

(0.395195, 0.735240)

(0.588527, 0.889734)

(0.264760, 0.604805)

(0.395195, 0.735240)

(0.441309, 0.776082)

(0.350413, 0.693065)

(0.441309, 0.776082)

(0.395195, 0.735240)

(0.488821, 0.815527)

(0.537839, 0.853466)

(0.350413, 0.693065)

(0.537839, 0.853466)

(0.488821, 0.815527)

(0.641141, 0.924076)

(0.641141, 0.924076)

(0.441309, 0.776082)

(0.488821,

...

...

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