Concept explainers
(a)
Find: that the fulfilled the assumptions and conditions needed for inference.
(a)
Explanation of Solution
There are told that both sample of men and women have been picked at random. Of all-American men and women aged 65 and older, 1012 males and 1062 females reflect less than 10 percent. It is fair to assume that both groups are independent, since the samples were chosen at random. There were 411 successes and 1011-411= 601 failures amongst these men, and there were 535 successes and 1062-535= 527 failures amongst these women. These numbers, for each group, are at least 10.
(b)
To Construct: a confidence interval of 95 percent for the difference in the proportions of older men and women who have the disease.
(b)
Answer to Problem 9E
(0.0550, 0.1404)
Explanation of Solution
Given:
Formula used:
Calculation:
Observed proportions are
Estimating the standard deviation
For a 95% confidence level,
Therefore, the 95% confidence interval is
A 95 percent confidence interval is (0.0550, 0.1404) for the difference in the proportions of older women and the mean that they suffered from some form of arthritis.
(c)
To Explain: the confidence interval.
(c)
Explanation of Solution
Depending on these samples, we are 95 percent sure that the real difference between 0.0550 and 0.1404 is the proportion of senior American women and American men who have suffered from any form of arthritis.
(d)
To Explain: that this confidence interval indicates that arthritis is more likely to affect women than men.
(d)
Explanation of Solution
A 95 % confidence interval is (0.0550. 0.1404) for the gap in the proportions of senior women and men who have suffered from certain form of arthritis. Since 0 is not part of the confidence interval, all limits are positive. The real difference in the proportions of senior American women and American men who have had any form of arthritis is not a reasonable value of 0. So, indeed, this confidence interval means that women are more likely to be affected by arthritis than men.
Chapter 22 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Additional Math Textbook Solutions
Elementary Statistics: Picturing the World (6th Edition)
Introductory Statistics
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Elementary Statistics (13th Edition)
Statistics for Business and Economics (13th Edition)
Essentials of Statistics (6th Edition)
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