(a)
Whether there is a 95% probability for the interval from 107.8 to 116.2 contains
(a)
Answer to Problem 18E
The explanation is incorrect.
Explanation of Solution
Given information:
95% confidence interval for the mean IQ:
(107.8, 116.2)
Since the confidence interval either contains or does not contain the population mean
Then
We know that the probability is either 0 or 1 (not 0.95).
Thus,
The explanation is incorrect.
(b)
Whether there is 95% chance for the interval (107.8, 116.2) contains
(b)
Answer to Problem 18E
The explanation is incorrect.
Explanation of Solution
Given information:
95% confidence interval for the mean IQ:
(107.8, 116.2)
Since the confidence interval always contains the sample mean.
Also,
Sample mean is the center of the confidence interval.
And
The probability is 1 instead of 0.95.
Thus,
The explanation is incorrect.
(c)
Whether the interval was constructed with method used to produce intervals for capturing the true mean in 95% of all possible samples.
(c)
Answer to Problem 18E
The explanation is correct.
Explanation of Solution
Given information:
95% confidence interval for the mean IQ:
(107.8, 116.2)
We know that
True mean is also known as population mean.
In this case,
The confidence interval of 95% of all possible samples will contain the true (population) mean.
Thus,
The explanation is correct.
(d)
Whether about 95% of the samples taken will contain the interval (107.8, 116.2).
(d)
Answer to Problem 18E
The explanation is incorrect.
Explanation of Solution
Given information:
95% confidence interval for the mean IQ:
(107.8, 116.2)
Since the samples will only contain the same confidence interval if the sample mean in the samples will be same.
Also,
The sample mean will be identical in a lot less than 95% of all possible samples.
Thus,
The explanation is incorrect.
(e)
Whether the probability for the interval (107.8, 116.2) captures
(e)
Answer to Problem 18E
The explanation is correct.
Explanation of Solution
Given information:
95% confidence interval for the mean IQ:
(107.8, 116.2)
Since the confidence interval either contains the population mean
Also,
The probability is either 1 or 0 (not 0.95).
Thus,
The explanation is correct.
Chapter 8 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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