10? -/2 points MIntroStat98E.062. My Notes During one particular war, the U.S. m

Question

10? -/2 points MIntroStat98E.062. My Notes During one particular war, the U.S. military was concerned about the nutrition of its recruits. Many did not have a sufficient number of teeth to chew the food provided to soldiers. As a result, it was likely that they would be undernourished and unable to fulfill their duties as soldiers. The requirements at that time specified that a recruit must have "at least four sound double teeth, one above and one below on each side of the mouth, and so opposed" so that they could chew food. Of the 58,552 recruits who were under the age of 20, 78 were rejected for this reason. For the 43,786 recruits who were 40 or over, 3,901 were rejected. (a) Find the proportion of rejects for each age group. (Round your answers to four decimal places.) age

Explanation / Answer

a)
Page<20 = 78/58552 = 0.0013

Page >40 = 3901/43786 = 0.0891

b)
n1 = 43786 , n2 = 58552

z value at 99% = 2.576

CI = ( p1 - p2) +/- z * sqrt(p1 * (1 -p1)/n1 + p2 * (1 -p2)/n2)
= ( 0.0891 - 0.0013) +/- 2.576 * sqrt(0.0891 * (1 -0.0891)/43786 + 0.0013 * (1 -0.0013)/58552)
= (0.0843,0.0913)

The 99% CI is (0.0843,0.0913)

c)
H0 :Page40 = Page20
Ha :Page40 not equals to Page20

d)
p = (3901 +78)/(43786+58552) = 0.0389

z = ( p1 - p2) / sqrt((p * (1 -p)(1/n1+ 1/n2))
= ( 0.0891 - 0.0013)/sqrt((0.0389 * (1 -0.0389)(1/43786 + 1/58552))
= 71.8713

P value = 0.00001.

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