Two-Sample Proportion zTest Say that 10 times, fast.

Minor differences Like with a 1-sample proportion zTest, we will use p instead of mu for our hypotheses. Like a 2-sample zTest, we will have two things equal to one another rather than a parameter equal to a number. Like so…

Minor differences (continued) Our z-calculation is only slightly more complex (as it is with a 2-sample zTest) For a 2-Proportion zTest we use… As noted yesterday, there is no tTest for proportions…remember, we create our own StD, and so we assume it to be the parameter StD.

Example on page 712 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 iners. In the year 1936, there were 223 deaths among 33,809 African miners and 7 deaths among 1541 European miners on the Gold Coast. – Consider this year as a sample from the pre-war era in Africa. Is there good evidence that the proportion of African miners who died was higher than the proportion of European miners who died?

P The parameter of interest is the proportion of African and European miners who died on the Gold Coast in the pre-war era.

H The proportion of African and European miners who died is equal. The proportion of African miners who died is greater than that of the Europeans.

A The problem states that we should consider this a random sample. We must assume that there were more than 3,308,090 African miners, and more than 15,410 European miners to continue For African miners np = 223 > 10,nq = >10 For European miners np = 7 10 While this does not satisfy the rule of thumb, we will proceed with caution.

N This is a 2-Proportion zTest

T

O P(z>1.16) = 1 – =

M We fail to reject the Ho, based on a p-value of 0.123, which is greater than our alpha of 0.05 or any reasonable alpha.

S We fail to reject the Ho, that the proportion of African miners who died is equal to the proportion of European miners who died on the Gold Coast in the pre-war era, based on a p-value of which is greater than our alpha of 0.05 or any reasonable alpha.