Concept explainers
(a)
To find: the standard error of the two-proportion difference.
(a)
Answer to Problem 12E
0.0682
Explanation of Solution
Given:
Formula used:
Calculation:
The standard error is
Therefore, the standard error in sample proportions is 0.0682
(b)
To construct: a 95 percent confidence interval.
(b)
Answer to Problem 12E
(0.1863, 0.4537) or (18.6%, 45.4%)
Explanation of Solution
Given:
From part (a) is
Formula used:
For 95 percent confidence interval
Calculation:
For 95 percent confidence interval
the critical value obtained is
Therefore,
Therefore, the 95 percent confidence interval for the difference in proportions occurred is (0.1863, 0.4537) or (18.6%, 45.4%)
(c)
To Explain: a suitable conclusion.
(c)
Explanation of Solution
The acquired outcome is as follows: After surgery, the 95 percent confidence interval for the difference in proportions of patients progressed and patients progressed after using wrist splints (18.6,45.4). So, among the recorded patients, 95 percent are positive. The number of patients who have surgery is between 18.6 percent and 45.4 percentage points higher than the percentage of patients who have wrist splints. And it is more likely that the surgery will be successful than wrist splints.
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