Question

A child dying from an accidental poisoning is a terrible incident. Is it more likely that a male child will get into poison than a female child? To find this out, data was collected that showed that out of 1830 children between the ages one and four who pass away from poisoning, 1031 were males and 799 were females (Flanagan, Rooney & Griffiths, 2005). does the data show that there are more male children dying of poisoning than female children? test at the 1% level

Answer 1

p1cap = X1/N1 = 1031/1830 = 0.5634
p1cap = X2/N2 = 799/1830 = 0.4366
pcap = (X1 + X2)/(N1 + N2) = (1031+799)/(1830+1830) = 0.5

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

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5634-0.4366)/sqrt(0.5*(1-0.5)*(1/1830 + 1/1830))
z = 7.67

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.

There is sufficient evidence to conclude that there are more male children dying of poisoning than female children