To find: The 95\% confidence interval for the comparison.

Caelan

Caelan

Answered question

2021-10-22

To find: The 95% confidence interval for the comparison.

Answer & Explanation

odgovoreh

odgovoreh

Skilled2021-10-23Added 107 answers

Calculation:
The study is conducted to see that whether a sample of children of different age groups consumed an adequate amount of calcium or not. In the study, samples are considered from two independent populations (different age groups).
First, the proportion of children aged 5 to 10 year who met the calcium requirement is defined by the formula:
p^1=CountSample size
Substitute the values in the above formula:
p^1=CountSample size
=8611055
=0.8161
Now, the proportion of children aged 11 to 13 years who met the calcium requirement is defined by the formula:
p^2=CountSample size
Substitute the values in the above formula:
p^2=CountSample size
=417974
=0.4281
The 95% confidence interval is defined by the formula:
CI=(p1p2)±zα2×PSKp1(1p1)n1+p2(1p2)n2
Substitute the values in the above formula:
CI=(p1p2)±zα2×PSKp1(1p1)n1+p2(1p2)n2
=(0.81610.4281)±1.96×0.8161(10.8161){1055}+0.4281(10.4281)974
=0.388±1.96×0.01983
=0.388±0.03886
=(0.3492,0.4268)
Hence, the required confidence interval is (0.3492, 0.4268).

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