Unformatted text preview: nfidence Intervals
True / False Questions 1611 Chapter 01  An Introduction to Business Statistics 1. The t distribution always has n degrees of freedom.
True False 2. When the margin of error is added to and subtracted from the sample mean an interval is
formed that will contain µ with probability of (1  α).
True False 3. The standard error of the sample mean is s/√n.
True False 4. Assuming the same level of significance α, as the sample size increases, the value of
tα/2approaches the value of zα/2.
True False 5. When constructing a confidence interval for a sample proportion, the t distribution is
appropriate if the sample size is small.
True False 6. First a 90% confidence interval is constructed from a sample size of 100. Then, for the
same identical data, a 92% confidence interval is constructed. The width of the 90% interval
is wider than the 92% confidence interval.
True False 1612 Chapter 01  An Introduction to Business Statistics 7. When the population is normally distributed and the population standard deviation σ is
unknown, then for any sample size n, the sampling distribution of
is based on the z
distribution.
True False 8. When the sample size and sample standard deviation remain the same, a 99% confidence
interval for a population mean, µ will be narrower than the 95% confidence interval for µ.
True False 9. 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.
True False 10. When the level of confidence and the sample size remain the same, a confidence interval
for a population mean µ will be wider, when the sample standard deviation s is small than
when s is large.
True False 11. When the level of confidence and sample proportion
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.
True False 12. When the level of confidence and sample size remain the same, a confidence interval for a
population proportion p will be narrower when
is larger than when
is
smaller.
True False 1613 Chapter 01  An Introduction to Business Statistics 13. 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
makes
as small as reasonably possible.
True False that 14. When determining the sample size n, if the value found for n is 79.2, we would choose to
sample 79 observations.
True False Multiple Choice Questions 15. The t distribution approaches the _______________ as the sample size ___________.
A. Binomial, increases
B. Binomial, decreases
C. Z, decreases
D. Z, increases 16. 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. 17. As standard deviation increases, samples size _____________ to achieve a specified level
of confidence.
A. Increases
B. Decreases
C. Remains the same 1614 Chapter 01  An Introduction to Business Statistics 18. 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 19. 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
_____ distribution.
A. z
B. t
C. Neither
D. Both A and B 20. A confidence interval increases in width as
A. The level of confidence increases
B. n decreases
C. s increases
D. All of the above 21. 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. 1615 is based on Chapter 01  An Introduction to Business Statistics 22. 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 23. 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 estimat...
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 Winter '14
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