Answered: survey was taken of randomly selected…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

418

1020

men and

541

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

be the sample proportion of senior women suffering from some form of arthritis, and let

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

nothing%

and

nothing%

▼

less

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.

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.

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