A Gallup poll asked the question, “Which of the following do you think is the pr

Question

A Gallup poll asked the question, “Which of the following do you think is the primary cause of gun violence in America – the availability of guns, the way parents raise their children, or the influences of popular culture such as movies, television, and the Internet?” Of the n = 493 men sampled, 250 answered “the availability of guns.” Of the 538 women sampled, 296 answered “the availability of guns.” Calculate a 99% confidence interval for pmen pwomen (make sure you also check data conditions). Write a sentence interpreting this interval in context.

Explanation / Answer

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 )=250
No.Of Observed (n1)=493
P1= X1/n1=0.507
Proportion 2
No. of chances(X2)=296
No.Of Observed (n2)=538
P2= X2/n2=0.55
C.I = (0.507-0.55) ±Z a/2 * Sqrt( (0.507*0.493/493) + (0.55*0.45/538) )
=(0.507-0.55) ± 2.58* Sqrt(0.001)
=-0.043-0.08,-0.043+0.08
=[-0.123,0.037]

INTERPRETATIONS      
Interpretations:
1) We are 99% sure that the interval [-0.123 , 0.037 ] 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, 99% of these intervals will contains the difference between
true population mean P1-P2
3) Since this Cl does contain a zero we can conclude at true mean
difference is zero  

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