weeks 9 through 12. 30 The Gold Coast. A historian examining Brit- ish colonial

Question

weeks 9 through 12. 30 The Gold Coast. A historian examining Brit- ish colonial records for the Gold Coast in Africa suspects that the death rate was higher among African miners than among European miners. In the year 1936, there were 223 deaths among 33,809 African miners and 7 deaths among 1541 European miners on the Gold Coast.24 (The Gold Coast became the independent nation of Ghana in 1957.) Consider this year as a random sample from the colonial era in West Africa. Is there good evi- dence that the proportion of African miners who died was higher than the proportion of European miners who died?

Explanation / Answer

Hyothesis:
H0 : p1 =p2
Ha : p1 > p2

test statistics:

p1 = 223/33809 = 0.0066, n1 = 33809
p2 = 7/1541 = 0.0045 ,n2 =1541

p = (p1 * n1 + p2 * n2) / (n1 + n2)
= ( 0.0066 *33809 + 0.0045 * 1541)/(33809 + 1541)
= 0.0065

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
= sqrt(0.0065 *(1-0.0065) * ((1/33809) + (1/1541)))
= 0.0021

z = (p1 - p2) / SE
= ( 0.0066 - 0.0045)/0.0021
= 1

p value = 0.1586

Do not reject the null hypothesis

There is not sufficient evidence to support the claim

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