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Stats 2

Submitted by britt85 on January 30, 2007

Category: Miscellaneous
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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 – 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 – 0.134722) – 0 / sqrt[(0.140155) x (1-0.140155) x (1/1342) x(1/720)]
= 0.008348 / 0.016037
= 0.520546

b)

Confidence Interval = (p1 – p2) +/- Zá/2 * [sqrt ((p1(1-p1)/n1) + p2(1-p2)/n2)]
= (0.143070 – 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, ......

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