survey was taken of randomly selected Americans, age 65 and older, which found that 418 of 1020 men and 541 of 1065 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.
survey was taken of randomly selected Americans, age 65 and older, which found that 418 of 1020 men and 541 of 1065 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.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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Question
A survey was taken of randomly selected Americans, age 65 and older, which found that
418
of
1020
men and
541
of
1065
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.
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.
No, it was not a random sample.
No, the groups were not independent.
No, more than 10% of the population was sampled.
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 for the difference in the proportions of senior men and women who have this disease,
p1−p2.
The confidence interval is
,.
(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
than the proportion of American men of the same age who suffer from arthritis.
nothing%
and
nothing%
▼
less
more
(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.
No, a conclusion cannot be made based on the confidence interval.
No, the interval is too close to 0.
Yes, the entire interval lies above 0.
Yes, there is 95% confidence, based on these samples, that about
nothing%
of senior women suffer from arthritis, while only
nothing%
of senior men suffer from arthritis.Expert Solution
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