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 2,028 children in the study. Here are the data. Age (years) Met requirement 5 to 10 11 to 13 No 196 553 Yes 861 418 Use a significance test to make the comparison. State the null and alternative hypotheses. H0: page 5-10 ? page 11-13 Ha: page 5-10 < page 11-13 H0: page 5-10 ? page 11-13 Ha: page 5-10 > page 11-13 H0: page 5-10 > page 11-13 Ha: page 5-10 ? page 11-13 H0: page 5-10 = page 11-13 Ha: page 5-10 ? page 11-13 Correct: Your answer is correct. Report the test statistic and the P-value. (Use p?age 5-10 ? p?age 11-13. Round your value for z to two decimal places and your P-value to four decimal places.) z = P-value =

Explanation / Answer

p=percentage of people consume adequate  calcium

a) H0: page 5-10 ? page 11-13 Ha: page 5-10 < page 11-13

H0=p1=p2 Ha: p1<p2

p1=0.8145,n1=1057

p2=0.4304,n2=971

p=0.6306

test statistics

z=

Z=(0.8145-0.4304)/sqrt(0.6306*(1-0.6306)*(1/1057+1/971))

p-value=p(z>17.90)

=0

b) H0: page 5-10 ? page 11-13 Ha: page 5-10 > page 11-13

z=

Z=(0.8145-0.4304)/sqrt(0.6306*(1-0.6306)*(1/1057+1/971))

p-value is 0 we reject null hypothesis

c) H0: page 5-10 > page 11-13 Ha: page 5-10 ? page 11-13

  page 5-10 = page 11-13 Ha: page 5-10 ? page 11-13

z=

Z=(0.8145-0.4304)/sqrt(0.6306*(1-0.6306)*(1/1057+1/971))

1-P(z<z test)=1

Here p-value is 1 we accept null hypothesis

d) page 5-10 = page 11-13 Ha: page 5-10 ? page 11-13

z=

Z=(0.8145-0.4304)/sqrt(0.6306*(1-0.6306)*(1/1057+1/971))

P(z<|z test|)=0

p-value is 0 we reject null hypothesis

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