A survey was taken of randomly selected Americans, age 65 and older, which found

Question

A survey was taken of randomly selected Americans, age 65 and older, which found that 405 of 1003 men and 548 of 1057 women suffered from some form of arthritis. a) Are the assumptions and conditions necessary for inference satisfied? Explain. b) Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease. c) Interpret your interval in this context. d) Does this suggest that arthritis is more likely to afflict women than men? Explain. a) Are the assumptions and conditions necessary for inference satisfied? Explain. O A. No, it was not a random sample. O B. No, the groups were not independent. ° C. No, more than 10% of the population was sampled. D. Yes, it was a random sample, less than 10% of the population was sampled, the groups were independent, and there were more than 10 successes and failures in each group b) Let p1 be the sample proportion of senior women suffering from some form of arthritis, and let p2 be the sample proportion of senior men suffering from some form of arthritis. Create a 95% confidence interval or the difference in the proportions of senior men and women who ave this disease. p 2 The confidence interval is Round to three decimal places as needed.)

Explanation / Answer

p2 = 405/1003 = 0.40, p1 = 548/1057 = 0.52.
n2 = 1003 , n1 = 1057

CI = ( p1 - p2) +/- z * sqrt( p1 *(1-p1)/n1 + p2 *(1-p2)/n2)
= ( 0.52 - 0.40) +/- 1.96 * sqrt(0.52 *( 1-0.52)/1057 + 0.40 * (1-0.40)/1003)
= (0.072,0.157)

The CI is (0.072,0.157)

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