Each of two groups consists of 100 patients who have leukaemia. A new drug is given to
the first group but not to the second (the control group). It is found that in the first
group 60 people have remission for 2 years; but only 40 in the second group. Find 95%
CI.
"\\hat{p}_2=\\dfrac{X_2}{N_2}=\\dfrac{40}{100}=0.4"
The critical value for "\\alpha = 0.05" is "z_c = z_{1-\\alpha\/2} = 1.96."
The corresponding confidence interval is computed as shown below:
"\\hat{p}_2-\\hat{p}_1+z_c\\sqrt{\\dfrac{\\hat{p}_1(1-\\hat{p}_1)}{N_1}+\\dfrac{\\hat{p}_2(1-\\hat{p}_2)}{N_2}})"
"=(0.6-0.4-1.96\\sqrt{\\dfrac{0.6(1-0.6)}{100}+\\dfrac{0.4(1-0.4)}{100}}"
"0.6-0.4+1.96\\sqrt{\\dfrac{0.6(1-0.6)}{100}+\\dfrac{0.4(1-0.4)}{100}})"
"=(0.0642, 0.3358)"
Therefore, based on the data provided, the 95% confidence interval for the difference between the population proportions "p_1-p_2" is "0.0642 < p_1 - p_2 < 0.3358," which indicates that we are 95% confident that the true difference between population proportions is contained by the interval "(0.0642, 0.3358)."
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