Confidence Intervals and Statistical Inference: Homework Assignments and Solutions Week 5
Practice problems on confidence intervals and statistical inference techniques.
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Confidence Intervals and Statistical Inference: Homework Assignments and
Solutions
Hamilton
Week 5 Homework
4. Why is a 99% confidence interval wider than a 95% confidence interval?
Solution)
The definition of a confidence interval is that it contains the true population mean. If I have a
95% confidence interval, that means I am 95% certain that the true population mean is in the
interval. If I want to be even more certain, I have to widen the interval. If I can be less certain, I
can narrow the interval.
So the widest interval will be 99%, and the narrowest would be 90%.
12. A person claims to be able to predict the outcome of flipping a coin. This person is correct
16/25 times. Compute the 95% confidence interval on the proportion of times this person can
predict coin flips correctly. What conclusion can you draw about this test of his ability to
predict the future?
Solution)
WE HAVE GIVEN THAT n = 25 and p = 16/25
And we need to construct the 95% C.I. for the proportion of times this person can predict coins
flips correctly as,
ṕ± 1.96 * √ (ṕq^/n)
=.64± 1.96 * √ (.64*.36/25)
= .64 ± .1882
So the 95% C.I. is,
(0.4518, 0.8282)
So We Are 95 Out Of 100 Attempts are confident that the values of the samples are lies b/w
(.4518,.8282)
15. You take a sample of 22 from a population of test scores, and the mean of your sample is
60.
(a) You know the standard deviation of the population is 10. What is the 99% confidence
interval on the population mean?
Solution)
Solutions
Hamilton
Week 5 Homework
4. Why is a 99% confidence interval wider than a 95% confidence interval?
Solution)
The definition of a confidence interval is that it contains the true population mean. If I have a
95% confidence interval, that means I am 95% certain that the true population mean is in the
interval. If I want to be even more certain, I have to widen the interval. If I can be less certain, I
can narrow the interval.
So the widest interval will be 99%, and the narrowest would be 90%.
12. A person claims to be able to predict the outcome of flipping a coin. This person is correct
16/25 times. Compute the 95% confidence interval on the proportion of times this person can
predict coin flips correctly. What conclusion can you draw about this test of his ability to
predict the future?
Solution)
WE HAVE GIVEN THAT n = 25 and p = 16/25
And we need to construct the 95% C.I. for the proportion of times this person can predict coins
flips correctly as,
ṕ± 1.96 * √ (ṕq^/n)
=.64± 1.96 * √ (.64*.36/25)
= .64 ± .1882
So the 95% C.I. is,
(0.4518, 0.8282)
So We Are 95 Out Of 100 Attempts are confident that the values of the samples are lies b/w
(.4518,.8282)
15. You take a sample of 22 from a population of test scores, and the mean of your sample is
60.
(a) You know the standard deviation of the population is 10. What is the 99% confidence
interval on the population mean?
Solution)
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Subject
Statistics