Confidence Intervals

Chapter 7
Confidence Intervals

True/False


1. The t distribution always has n degrees of freedom.
Answer: False Difficulty: Easy


2. Assuming the same level of significance α, as the sample size increases, the value of tα/2
approaches the value of zα/2.
Answer: True Difficulty: Medium


3. When constructing a confidence interval for a sample proportion, the t distribution
is appropriate if the sample size is small.
Answer: False Difficulty: Medium


4. When the population is normally distributed and the population standard deviation 
is unknown, then for any sample size n, the sampling distribution of X is based on the z
distribution.
Answer: False Difficulty: Medium (REF)


5. When the sample size and sample standard deviation remain the same, a 99%
confidence interval for a population mean,  will be narrower than the 95% confidence
interval for . Answer: False Difficulty: Medium (REF)


6. When the level of confidence and sample standard deviation remain the same, a confidence
interval for a population mean based on a sample of n = 100 will be narrower than a confidence
interval for a population mean based on a sample of n = 50.
Answer: True Difficulty: Medium


7. When the level of confidence and the sample size remain the same, a confidence interval for
a population mean  will be wider, when the sample standard deviation s is small than when s is
large.
Answer: False Difficulty: Medium




1

,Confidence Intervals




8. When the level of confidence and sample proportion p remain the same, a confidence
interval for a population proportion p based on a sample of n = 100 will be wider than a
confidence interval for p based on a sample of n = 400.
Answer: True Difficulty: Medium


9. When the level of confidence and sample size remain the same, a confidence interval for a
population proportion p will be narrower when pˆ (1 is larger than pˆ (1 is smaller.
Answer: False Difficulty: Medium (REF) pˆ) when pˆ)


10. When solving for the sample size needed to compute a 95% confidence interval for a
population proportion “p”, having a given error bound “B”, we choose a value of that makes
pˆ
pˆ (1 as small as reasonably possible.
pˆ)
Answer: False Difficulty: Medium (REF)


11. When determining the sample size n, if the value found for n is 79.2, we would choose
to sample 79 observations.
Answer: False Difficulty: Medium (REF)


Multiple Choice


12. The t distribution approaches the as the sample size .
A) Binomial, increases
B) Binomial, decreases
C) Z, decreases
D) Z, increases
Answer: D Difficulty: Medium (REF)


13. The width of a confidence interval will be:
A) Narrower for 99% confidence than 95% confidence.
B) Wider for a sample size of 100 than for a sample size of 50.
C) Narrower for 90% confidence than 95% confidence.
D) Wider when the sample standard deviation (s) is small than when s is
large. Answer: C Difficulty: Medium




Bowerman, Essentials of Business Statistics, 2/e 2

,Confidence Intervals




14. As standard deviation increases, samples size to achieve a specified level of
confidence.
A) Increases
B) Decreases
C) Remains the same
Answer: A Difficulty: Medium


15. When determining the sample size, if the value found is not an integer initially, the
next highest integer value will be chosen.
A) Always
B) Sometimes
C) Never
Answer: A Difficulty: Medium


16. When constructing a confidence interval for a population mean, if a population is
normally distributed and a small sample is taken, then the distribution of X is based on
distribution.
A) z
B) t
C) Neither
D) Both A and B
Answer: B Difficulty: Medium


17. A confidence interval increases in width as
A) The level of confidence increases
B) n decreases
C) s increases
D) All of the above
Answer: D Difficulty: Medium (REF)


18. The width of a confidence interval will be:
A) Narrower for 98% confidence than for 90% confidence.
B) Wider for a sample size of 64 than for a sample size of 36.
C) Wider for a 99% confidence than for 95% confidence
D) Narrower for sample size of 25 than for a sample size of 36.
E) None of the above
Answer: C Difficulty: Medium




Bowerman, Essentials of Business Statistics, 2/e 194

, 19. A Research and Development Laboratory researcher for a paint company is measuring the
level a certain chemical contained in a certain type of paint. If the paint contains too much of
this chemical, the quality of the paint will be compromised. On the average, each can of paint
contains 10% of the chemical, How many cans of paint should the sample contain if the
researcher wants to be 98% certain of being within 1% of the true proportion of this chemical?
A) 4887
B) 1107
C) 26
D) 645
Answer: A Difficulty: Medium (AS)


20. Which of the following is an advantage of confidence interval estimate over a point
estimate for a population parameter?
A) Interval estimates are more precise than point estimates.
B) Interval estimates are less accurate than point estimates.
C) Interval estimates are both more accurate and more precise than point estimates.
D) Interval estimates take into account the fact that the statistic being used to estimate
the population parameter is a random variable.
Answer: D Difficulty: Medium


21. When the sample size and sample standard deviation remain the same, a 99% confidence
interval for a population mean,  will be the 95% confidence interval for .
A) Wider than
B) Narrower than
C) Equal to
Answer: A Difficulty: Medium (REF)


22. When the level of confidence and sample standard deviation remain the same, a
confidence interval for a population mean based on a sample of n = 100 will be a
confidence interval for a population mean based on a sample of n = 50.
A) Wider than
B) Narrower than
C) Equal to
Answer: B Difficulty: Medium


23. When the level of confidence and the sample size remain the same, a confidence interval
for a population mean  will be , when the sample standard deviation s is small
than when s is large.
A) Wider
B) Narrower
C) Neither A nor B, they will be the
same Answer: B Difficulty: Medium



195 Bowerman, Essentials of Business Statistics, 2/e