A historian examining British colonial records for the Gold Coast in Africa susp

Question

A historian examining British 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 232 deaths among 33751 African miners and 7 deaths among 1531 European miners on the Gold Coast. Consider this year as a random sample from the colonial era in West Africa. Is there good evidence that the proportion of African miners who died was higher than the proportion of European miners who died? Solving the problem step by step, find the following values:

The sample proportion (±0.00001) for African miners: = .

The sample proportion (±0.00001) for European miners: = .

The pooled proportion (±0.00001): :

The standard error (±0.0001) of the statistic : .

The z test statistic (±0.01): .

Is there good evidence significant at ? No Yes

Explanation / Answer

For African Miners, p1 = 232/33751 = 0.006874. q1 = 1 -p1 =

For European Miners, p2 = 7/1531 = 0.004572, q2 = 1-p2 =

To test the null hypothesis H0: p1 = p2 against the alternative hypothesis H1: p1  p2

As the sample size is quite large we can take Z-statistic that is Z = p1 - p2 / (p1q1/n1 + p2q2/n2)

=(0.006874-0.004572) / (0.006874*0.993126/33751 + 0.004572*0.995428/1531) = 1.29

The value of Z at 0.05 level of significance is 1.96 and at 0.01 level is 2.58. As such the hypothesis that there is no difference between the proportion of deaths between the miners of Africa and Europe is accepted.

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