Answer:
There is no enough statistical evidence that the proportion of African miners deaths is higher than Europeans.
Step-by-step explanation:
We want to perform a hypothesis test on the difference of proportions.
The null and alternative hypothesis are:
[tex]H_0: \pi_1=\pi_2\\\\ H_1: \pi_1\neq\pi_2[/tex]
We assume a level of significance of 0.05.
The proportion of European miners that died in 1936 is:
[tex]p_1=7/1541=0.0045[/tex]
The proportion of African miners that died in 1936 is:
[tex]p_1=223/33809=0.0066[/tex]
The difference in proportions is
[tex]\Delta p =p_2-p_1=0.0066-0.0045=0.0021[/tex]
The weighted average of the proportion to estimate the standard deviation is:
[tex]p=\frac{n_1*p_1+n_2*p_2}{n_1+n_2}=\frac{1541*0.0045+33809*0.0065}{1541+33809}=\frac{7+223}{1541+33809}=\frac{230}{35350}=0.0065[/tex]
The estimated standard deviation is:
[tex]s=\sqrt{\frac{p(1-p)}{n_1}+\frac{p(1-p)}{n_2}}=\sqrt{\frac{0.0065*0.9935}{1541}+\frac{0.0065*0.9935}{33809}}=0.0021[/tex]
The z-value can now be calculated
[tex]z=(p_2-p_1)/s=(0.0066-0.0045)/0.0021=1[/tex]
The P-value for z=1 is
[tex]P(z>1)=0.32[/tex]
The P-value (0.32) is greater than the significance level (0.05), so we failed to reject the null hypothesis.
There is no evidence the proportion of African miners deaths is higher than Europeans.
