Researchers would like to know whether the proportions of elementary school chil

Question

Researchers would like to know whether the proportions of elementary school children who are obese differ in rural and urban area. An earlier study found that 45% of urban school children and 40% of rural school children are obese. The researchers select 183 urban school children and 238 rural school children. Suppose [^(p)]1 and [^(p)]2 denote sample proportions of urban and rural school children respectively who are obese.

Answer all the questions below (where appropriate) as a fraction not as a percentage.

a)What is the expected proportion of obese among urban school children, i.e. expected value of [^(p)]1? [Answer to two decimal places.]

b)What is the standard deviation of proportion of obese among urban school children, i.e. ?([^(p)]1)? [Answer to four decimal places.]

c)What is the expected proportion of obese among rural school children, i.e. expected value of [^(p)]2? [Answer to two decimal places.]

d)What is the standard deviation of proportion of obese among rural school children, i.e. ?([^(p)]2)? [Answer to four decimal places.]

e)What is the expected difference of proportions of obese between urban and rural school children, i.e. expected value of [^(p)]1 ? [^(p)]2? [Answer to two decimal places.]

f)What is the standard deviation of difference of proportions of obese between urban and rural school children, i.e. ?([^(p)]1 ? [^(p)]2)? [Answer to four decimal places.]

g)What is the probability that the difference of proportions of obese between urban and rural school children will be larger than 0.08? i.e. find P([^(p)]1 ? [^(p)]2 > 0.08). [Answer to four decimal places.]

Explanation / Answer

Since no other data is provided, so we will use the data of the previous research to estimate the proportions.

(a)

Estimated value of p'1 = 0.45

(b)

Standard deviation of proportion of obese urban people = (p'1*(1-p'1)/n1)^0.5 = (0.45*(1-0.45)/183)^0.5 = 0.0368

(c)

Estimated value of p'2 = 0.40

(d)

Standard deviation of proportion of obese rural people = (p'2*(1-p'2)/n2)^0.5 = (0.4*(1-0.4)/238)^0.5 = 0.0317

(e)

Expected difference of proportions = p'1-p'2 = 0.45-0.40 = 0.05

(f)

Standard deviation of difference of proportions of obese rural people = (p'1*(1-p'1)/n1+ p'2*(1-p'2)/n2)^0.5 = (0.45*(1-0.45)/183 + 0.4*(1-0.4)/238)^0.5 = 0.0486

(g)

First we calculate the z-score:

z = (0.08-0.05)/0.0486 = 0.6172

The corresponding p-value for this z-value is as follows:

p = 0.2686

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.