a.
Show that
Derive the
a.
Answer to Problem 59SE
It is verified that
The
Explanation of Solution
Given info:
A random sample
Calculation:
Let
The probability density function of the random variable
Probability value:
Therefore, it is verified that
Confidence interval based on given probability statement:
The confidence interval for
Thus, the
b.
Show that
Derive the
b.
Answer to Problem 59SE
It is verified that
The
Explanation of Solution
Calculation:
Let
The probability density function of the random variable
Probability value:
Therefore, it is verified that
Confidence interval:
The confidence interval for
Thus, the
c.
Find the shorter interval among the obtained two intervals.
Find the 95% confidence interval for
c.
Answer to Problem 59SE
The confidence interval obtained in part (b) is shorter than the interval obtained in part (a).
The 95% confidence interval for
Explanation of Solution
Given info:
The data represents the sample of 5 waiting times of a morning bus. The variable waiting time for a morning bus is uniformly distributed.
Calculation:
The confidence interval for
Width of the confidence interval obtained in part (b):
The confidence interval for
Width of the confidence interval obtained in part (b):
Here, the value of
That is,
And the sample size n will be always greater than 1.
That is,
From this it can be said that,
Therefore, the width of the interval in part (b) will be narrower than the width of the interval in part (a).
Thus, the shorter confidence interval for
95% confidence interval:
For 95% confidence level,
Thus, the level of significance is
The maximum waiting time for a sample of 5 waiting times is
The 95% confidence interval for
Thus, the 95% confidence interval for
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Chapter 7 Solutions
Probability and Stats. for Engineering.. (Looseleaf)
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