Starting in the 1970s, medical technology allowed babies with very low birth wei

Question

Starting in the 1970s, medical technology allowed babies with very low birth weight (VLBW, less than 1500 grams, about 3.3 pounds) to survive without major handicaps. It was noticed that these children nonetheless had difficulties in school and as adults. A long-term study has followed 249 VLBW babies to age 20 years, along with a control group of 225 babies from the same population who had normal birth weight. Of the 132 women in the VLBW group, 40 said they had used illegal drugs; 55 of the 120 control group women had done so. The test statistic for testing a null hypothesis of no difference with the VLBW women as group 1 is z = (±.001) and the P-value is (±.0001) Is this difference between the two groups statistically significant at =0.01

Explanation / Answer

Data:    

n1 = 132   

n2 = 120   

p1 = 0.303030303   

p2 = 0.458333333   

Hypotheses:    

Ho: p1 = p2    

Ha: p1 p2    

Decision Rule:    

= 0.01   

Lower Critical z- score =   -2.575829304

Upper Critical z- score = 2.575829304

Reject Ho if |z| >   2.575829304

Test Statistic:    

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (132 * 0.303030303030303 + 120 * 0.458333333333333)/(132 + 120) = 0.376984127

q = 1 - p = 1 - 0.376984126984127 = 0.623015873

SE = [pq * {(1/n1) + (1/n2)}] = (0.376984126984127 * 0.623015873015873 * ((1/132) + (1/120))) = 0.061127097

z = (p1 - p2)/SE = (0.303030303030303 - 0.458333333333333)/0.0611270968203843 = -2.541

p- value = 0.0111   

Decision (in terms of the hypotheses):    

Since 2.540657718 < 2.575829304 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence of a difference between the population proportions.

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