Young children need calcium in their diet to support the growth of their bones.

Question

Young children need calcium in their diet to support the growth of their bones. The Institute of Medicine provides guidelines for how much calcium should be consumed by people of different ages. One study examined whether or not a sample of children consumed an adequate amount of calcium based on these guidelines. Since there are different guidelines for children aged 5 to 10 years and those aged 11 to 13 years, the children were classified into these two age groups. Each student's calcium intake was classified as meeting or not meeting the guideline. There were 2,037 children in the study. Here are the data.

Report the test statistic and the P-value. (Use page 5-10 page 11-13. Round your value for z to two decimal places and your P-value to four decimal places.)

z=

P-value=

PLEASE SHOW ME HOW TO FIND Z WITHOUT SOFTWARE AS I AM REQUIRED TO DO THIS BY HAND AND NEED TO UNDERSTAND IT.

Explanation / Answer

Given that,
sample one, x1 =199, n1 =199+869= 1068, p1= x1/n1=0.186
sample two, x2 =556, n2 =556+413 = 969, p2= x2/n2=0.574
Hypotheses: H0:p1-p2=0 (there is no difference in population proportion of two groups of children who met the calcium intake requirement)
H1:p1-p2=/=0 (there is difference in population proportion of two groups of children who met the calcium intake requirement).
level of significance, = 0.025
from standard normal table, two tailed z /2 =2.241
since our test is two-tailed
reject Ho, if zo < -2.241 OR if zo > 2.241
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.186-0.574)/sqrt((0.371*0.629(1/1068+1/969))
zo =-18.082
| zo | =18.082
critical value
the value of |z | at los 0.025% is 2.241
we got |zo| =18.082 & | z | =2.241
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -18.0821 ) = 0
hence value of p0.025 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -18.082
critical value: -2.241 , 2.241
decision: reject Ho
p-value: 0

there is difference in population proportion of two groups of children who met the calcium intake requirement

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