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SOLUTIONS
_____a_____ (1) Which of the following would widen the confidence interval estimator of the population
mean?
_____d_____ (2) Suppose that you correctly set up a null and research hypothesis and correctly calculate a
p-value of 0.95. Which of the following should you conclude?
_____b_____ (3) Suppose you wanted to show that the demand for Diet Sprite (a soft drink) is elastic.
Which of the following correctly specifies the null and research hypotheses?
_____a_____ (4) Suppose you set up the following hypotheses to make an inference about an unknown
population proportion:
_____c_____ (5) Consider a hypothesis test about an unknown population mean assuming the population
s.d. is known. When would the probability of a Type I Error be the smallest?
_____d_____ (6) Based on only this information you should infer that:
_____b_____ (7) What is the 95% confidence interval estimator of the population mean?
_____a_____ (8) What is the 95% confidence interval estimator of the population variance?
_____b_____ (9) Consider hypothesis testing about an unknown population proportion. In which case
would it be appropriate to assume the test statistic is approximately normal?
_____b_____ (10) At the standard significance level (α = 0.05), what should you infer?
____c______ (11) What is the p-value?
____d______ (12) Which graph shows the probability of Type II error when the true population proportion is
0.56 and Type I error is 0.05?
_____b_____ (13) At the standard significance level (α = 0.05), which of the following would be the
appropriate rejection region for a two-tailed hypothesis test about the population mean assuming the
population variance is unknown and the sample size is very very large?
_____a_____ (14) Suppose X is a random variable measuring the hourly wage of employees. Suppose X
has mean = $10 per hour and s.d. = $2 per hour. If all employees work full-time (40 hours per week), what
is their average weekly salary and the s.d. of their weekly salary?
_____d_____ (15) For which of the following samples would it be appropriate to use the Student t tables for
the purpose of constructing a 95% confidence interval estimator of the population mean?
_____F_____ (1) Both the standard normal and chi-squared distributions are symmetric.
_____F_____ (2) The value of the population parameter specified in the null hypothesis (H0) is the center
point of a confidence interval estimator.
_____F_____ (3) Sample statistics calculated from sufficiently small samples are biased.
_____F_____ (4) Sample statistics calculated from sufficiently large samples are unbiased.
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_____F_____ (5) If X and Y are independent standard normal random variables then X+Y is also a
standard normal random variable.
_____T_____ (6) The normal distribution is a two parameter distribution.
_____T_____ (7) Other things equal, the standard error of the sample mean decreases as the sample size
increases.
_____T_____ (8) The sample mean is a consistent estimator of the population mean.
_____T_____ (9) Suppose you have 200 different random samples. If for each sample you estimate a 95
percent confidence interval for the population mean, you would expect that for 10 of the samples the
estimated confidence interval would exclude the true population mean.
_____F_____ (10) A population parameter is a random variable.
_____T_____ (11) Other things equal, increasing the sample size decreases the width of a confidence
interval estimator.
_____F_____ (12) The sample median is a biased estimator of the population mean.
_____T_____ (13) Other things equal, to estimate the sample mean within 2 units, you would need to
collect a larger sample from a population with σ=4 compared to a population with σ=2.
_____F_____ (14) Suppose a researcher conducts two separate hypothesis tests and the sample, test
statistic, and significance level are exactly the same for both tests. It is not possible for a researcher to fail
to reject the null in a two-tailed test but succeed in rejecting the null in a one-tailed test.
_____F_____ (15) If X and Y are independent normal random variables then Z = X / Y is another normal
random variable.
_____F_____ (16) The probability of a Type I error is greater if two-tailed hypothesis testing is conducted
using a 99% confidence interval estimate rather than a 95% confidence interval estimate.
_____T_____ (17) The probability of a Type II error is greater if two-tailed hypothesis testing is conducted
using a 99% confidence interval estimate rather than a 95% confidence interval estimate.
_____F_____ (18) Type II errors are more likely when the null hypothesis provides a very unrealistic
description of the population.
_____F_____ (19) If you wanted to accurately estimate the proportion of voters who voted for Ralph Nader
(an unpopular candidate) in the 2000 U.S. Presidential election you would need a larger sample size than
you would to estimate the proportion who voted for George W. Bush (a more popular candidate).
_____T_____ (20) Non-response bias could cause a 90 percent confidence interval estimator to exclude
the true population parameter much more than 10 percent of the time.
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