A survey was taken of randomly selected Americans, age 65 and older, which found that 420 of 1002 men and 543 of 1068 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.

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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
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A survey was taken of randomly selected Americans, age 65 and older, which found that 420 of 1002 men and 543 of 1068 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.
Transcribed Image Text:A survey was taken of randomly selected Americans, age 65 and older, which found that 420 of 1002 men and 543 of 1068 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.
b) Let p, be the sample proportion of senior women suffering from some form of arthritis, and let p, be the sample proportion of senior men suffering from some form of arthritis. Create a 95% confidence interval for the difference in
the proportions of senior men and women who have this disease, p, - p2.
The confidence interval is ( D).
(Round to three decimal places as needed.)
%
c) There is 95% confidence, based on these samples, that the proportion of American women, age 65 and older, who suffer from arthritis is between % and
than the proportion of American men of the same age who
suffer from arthritis.
(Round to one decimal place as needed.)
d) Does this suggest that arthritis is more likely to afflict women than men? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
A. No, the interval is too close to 0.
B. No, a conclusion cannot be made based on the confidence interval.
O C. Yes, the entire interval lies above 0.
D. Yes, there is 95% confidence, based on these samples, that about
% of senior women suffer from arthritis, while only
% of senior men suffer from arthritis.
(Round to one decimal place as needed.)
Transcribed Image Text:b) Let p, be the sample proportion of senior women suffering from some form of arthritis, and let p, be the sample proportion of senior men suffering from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease, p, - p2. The confidence interval is ( D). (Round to three decimal places as needed.) % c) There is 95% confidence, based on these samples, that the proportion of American women, age 65 and older, who suffer from arthritis is between % and than the proportion of American men of the same age who suffer from arthritis. (Round to one decimal place as needed.) d) Does this suggest that arthritis is more likely to afflict women than men? Select the correct answer below and, if necessary, fill in the answer boxes within your choice. A. No, the interval is too close to 0. B. No, a conclusion cannot be made based on the confidence interval. O C. Yes, the entire interval lies above 0. D. Yes, there is 95% confidence, based on these samples, that about % of senior women suffer from arthritis, while only % of senior men suffer from arthritis. (Round to one decimal place as needed.)
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