Concept explainers
a.
Show that for a proportion
a.
Explanation of Solution
Given info:
Consider X represents the number of
Calculation:
Here, X follows normally distributed with mean
Multiply by −1 on both sides in the above inequalities.
Add X on both sides in the above inequalities.
Hence, a proportion
b.
Show that
b.
Explanation of Solution
Given info:
Calculation:
Here, n is constant, then
Thus,
c.
Conclude that for a proportion
c.
Explanation of Solution
Calculation:
From part (a),
Divide the above inequality by n.
Thus, a proportion
d.
Derive the expression for the level
d.
Explanation of Solution
Given info:
Calculation:
From part (c),
Substitute
Thus, the expression for the level
e.
Find the 95% confidence interval for
e.
Answer to Problem 19SE
The 95% confidence interval for
Explanation of Solution
Given info:
Calculation:
The value of
The value of
From Table A.2 of the Cumulative Normal distribution, the value of
The 95% confidence interval for
Thus, the 95% confidence interval for
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Chapter 5 Solutions
Statistics for Engineers and Scientists
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