Question

3. Childhood obesity: A national healthy survey weighed a sampled of 546 boys aged 6-11 and found that 74 of them were overweight. They weighed a sample of 455 girls aged 6-11 and found that 75 of them were overweight a) State the null and alternate hypothesis b) What is the significant level? c) Compute the p-value d) Do you reject the null hypothesis? Explain? e) Can you conclude that the proportion of boys who are overweight is less than the proportion of girls who are overweight? Use the a-0.10 level of significance

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

b)

0.10 is the significance level

c)
p1cap = X1/N1 = 74/546 = 0.1355
p2cap = X2/N2 = 75/455 = 0.1648
pcap = (X1 + X2)/(N1 + N2) = (74+75)/(546+455) = 0.1489

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1355-0.1648)/sqrt(0.1489*(1-0.1489)*(1/546 + 1/455))
z = -1.30

P-value Approach
P-value = 0.0974

d)

As P-value < 0.1, reject the null hypothesis.

e)

yes, we can conclde