The Diabetes Control and Complications Trial followed diabetes patients diagnose

Question

The Diabetes Control and Complications Trial followed diabetes patients diagnosed with retinopathy before joining the study They were randomly assigned to one of two treatments and monitored for 6 years The study found that 153 of the 336 patients assigned to the conventional treatment showed a sustained progression of their original retinopathy. In contrast, only 68 of the 375 patients assigned to the intensive treatment had sustained retinopathy progression. Find a point estimate of the difference between the proportion of conventional treatment patients with sustained retinopathy progression and the proportion of intensive treatment patients with sustained retinopathy progression (Use 3 decimal places) A 95% confidence interval for the difference in the two proportions, p_1 - P_2, is (0 208, 0 340). What does this mean? Because the interval contains 0, there is enough evidence at the 0 05 level to conclude that the two proportions are significantly different. Because the interval contains 0, there is not enough evidence at the 0 05 level to conclude that the two proportions are significantly different. Because the interval does not contain 0, there is enough evidence at the 0 05 level to conclude that the two proportions are significantly different. Because the interval does not contain 0, there is not enough evidence at the 0 05 level to conclude that the two proportions are significantly different

Explanation / Answer

b.
Confidence Interval for Diffrence of Proportion
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No. of chances( X1 )=153
No.Of Observed (n1)=336
P1= X1/n1=0.455
Proportion 2
No. of chances(X2)=68
No.Of Observed (n2)=375
P2= X2/n2=0.181
C.I = (0.455-0.181) ±Z a/2 * Sqrt( (0.455*0.545/336) + (0.181*0.819/375) )
=(0.455-0.181) ± 1.96* Sqrt(0.001)
=0.274-0.066,0.274+0.066
=[0.208,0.34]
Interpretations:
1) We are 95% sure that the interval [0.208 , 0.34 ] contains the difference between
true population proportion P1-P2
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the difference between
true population mean P1-P2
3) Since this Cl does n't contain a zero we can conclude at true proportion
difference is not zero      

because the interval does not contain zero , there is enough evidence at the 0.05 level
of confidence that two proportions are significantly diffrent

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