Reading and Comprehension Questions for Chapter 8
1. The statistical interval that contains a stated proportion of the values of a probability
distribution is called a confidence interval.
True False
False – this is the definition of a tolerance interval.
2. In a 95% confidence interval the quantity 0.05 = 1 – 0.95 is called the confidence
coefficient.
True False
True.
3. If a 95% confidence interval on the mean has a lower limit of 10 and an upper limit of
15, this implies that 95% of the time the true value of the mean is between 10 and 15.
True False
False – this is the wrong interpretation of a confidence interval. This specific interval is
either correct or incorrect. If a large number of such intervals are constructed, 95% of
them will contain the true value of the mean.
4. For a fixed value of the standard deviation and a fixed sample size, a confidence
interval on the population mean will get longer as the level of confidence increases from
96% to 99%.
True False
True
5. The length of a confidence interval is a measure of precision of estimation.
True False
True
6. For a fixed value of the standard deviation, a 95% confidence interval on the
population mean will get shorter if the sample size increases.
True False
True
7. As the standard deviation increases the sample size required for a fixed length
confidence interval on the mean increases.
True False
True
8. The upper one-sided 95% confidence bound an the mean of a normal distribution will
always be greater than the upper bound on the mean from a two-sided 95% confidence
interval.
True False
False – the lower bound is always less than the two-sided upper confidence limit,
assuming equal confidence.
9. The interval
x  z / 2
s
s
   x  z / 2
n
n
can be used as a large-sample confidence interval for the mean regardless of the
population distribution so long as the sample size n is at least 40.
True False
True
10. The quantity
T
X 
S/ n
has a t-distribution with n – 1 degrees of freedom if the sample mean is computer from a
random sample of size n from a normal distribution.
True False
True
11. A t-CI on the mean will be the same length as a z-CI on the mean if the sample
standard deviation is equal to the population standard deviation  .
True False
False – Note that the percentage points of t are always greater than or equal to the
corresponding percentage points of the standard normal distribution; therefore, the t-CI
on the mean will be longer than a z-CI on the mean as long as the degrees of freedom are
less than infinity.
12. If S2 is the sample variance of a random sample of size n from a normal distribution,
the random variable (n  1) S 2 /  2 has a chi-square distribution with n – 1 degrees of
freedom.
True False
True
13. The CI on the variance of a normal distribution makes use of the chi-square
distribution.
True False
True
14. The normal approximation to the binomial can be use to construct a CI on a
population proportion.
True False
True
15. The sample size required for constructing a CI on a population proportion that has a
specified error n estimation depends on the unknown proportion, p.
True False
True
16. The length of a 95% CI on the proportion p will be longer if p= 0.1 than if p = 0.5.
True False
False – the variance of the binomial distribution is maximum when p = 0.5, so the 95%
CI when p = 0.5 will be longer than the 95% CI when p = 0.1.
17. The prediction interval for a future observation from a normal distribution will always
be longer than the CI on the mean of the normal distribution.
True False
True
18. As the sample size gets large (approaching infinity) the length of a CI on the mean
approaches the length of the prediction interval.
True False
False – as n approaches infinity the length of a CI approaches zero.
19. As the sample size gets large (approaching infinity) the length of a prediction interval
on a future observation approaches zero.
True False
False – as n approaches infinity the uncertainty in estimating the mean goes to zero, but
the uncertainty associated with the future observation remains. Therefore, even with an
infinite sample size the prediction interval will not have length zero.
20. A tolerance interval is a statistical interval that captures a fixed proportion of the
population values.
True False
True