is the temporary cessation of breathing, and it can result in death or severe di
ID: 3267678 • Letter: I
Question
is the temporary cessation of breathing, and it can result in death or severe disability in premature In a international study, a random sample of 937 premature babies received a caffeine therapy, and a random sample of 932 premature babies received a placebo therapy. Of the babies who received the caffeine therapy, 377 suffered death or disability. Of the babies who received the placebo therapy, 431 suffered death 3 or disability. Does the data support the claim that caffeine lowers the rate of death or severe disability resulting from apnea premature babies? Use a 5% level significance. a. Write in words what p_1 and p_2, represents in this problem. Let p_1 = Let p_2 = b. Write down the null and alternative hypotheses for this test using correct symbols. H_0: _____ H_a: _____ c. Test used: d. Give the test statistic and the p-value Test statistic = _____ p-value = _____ e. State your decision. g. State your conclusion.Explanation / Answer
Let:
p1 = proportion of death in babies receiving placebo therapy
p2 = proportion of death in babies receiving caffeine therapy
The hypotheses are:
H0: p1-p2 = 0
Ha: p1-p2 > 0
Given data:
p1 = 431/932 = 0.462, n1 = 932
p2 = 377/937 = 0.402, n2 = 937
Pooled proportion, p = (p1n1 + p2n2)/(n1+n2) = (431+377)/(932+937) = 0.432
Calculating standard error:
SE = ( p*(1-p)*(1/n1 + 1/n2) )0.5 = ( 0.432*(1-0.432)*(1/932 + 1/937) )0.5 = 0.023
Calculating test statistic:
z = (p1-p2)/SE = (0.462-0.402)/0.023 = 2.608
The corresponding p-value for this z-score is:
p = 0.0045
At significance level of a = 0.05,
Since p < a, so we reject the null hypothesis.
The data shows enough evidence that caffeine therapy lowers the death rate.
Hope this helps !
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