Problems: Review of Univariate Statistics
2
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___1. The reason for taking a random sample is to
eliminate:
 a) chance error.
 b) error from bias.
 c) standard error.
 d) all error.
___2. Even when a sample is drawn correctly, the estimate
we get from a sample will usually differ a bit from the
value we are trying to estimate because of:
 a) chance error.
 b) error from bias.
 c) mathematical error.
 d) correlation error.
___3. The reliability of an estimate is better when the
variation in the population is:
 a) small and the sample size is small.
 b) large and the sample size is large.
 c) small and the sample size is large.
 d) large and the sample size is small.
___4. The giveortake number:
 a) tells us how accurate our estimate of the mean or
percentage is.
 b) gives us a value from the normal table.
 c) gives us a value from the t table.
 d) is the same as the standard deviation of the
population.
___5. Another name for the giveortake number is:
 a) the mean.
 b) the average.
 c) the standard error of estimate.
 d) N, the sample size.
___6. A pollster has estimated the popularity of the
president and finds that his approval rating is 45%. Another
pollster, using the same questions and methods, estimates
that it is 49%. How should we explain this discrepancy?
 a) It is due to bias.
 b) It is due to chance error.
 c) It shows one or maybe both of these pollsters made
a mistake in their procedures.
 d) It shows that at least one of them is
deceitful.
___7. A research paper states, "The 95% confidence
interval for weight is 103 to 112 pounds." Which of the
following is the best interpretation of this statement?
 a) There is a 95% chance that the true average weight
is between 103 and 112 pounds.
 b) 95% of all weights in the population are between
103 and 112 pounds.
 c) 95% of all weights in the sample are between 1003
and 112 pounds.
 d) The researcher has used a procedure that works 95%
of the time, so he is 95% confident that he has found the
population weight.
8. If you a die 240 times, how many sixes would you
expect to get? Suppose you get 50. Is this enough so that
you would conclude that the die is not a fair die? (Hint:
Use the box model to compute the standard error of the sum,
and then find the zscore of 50. How likely is it to be this
far away from or further from the expected value?)
9. We have discussed how statistical inference resembles
a trial by jury. Let's work though a simple problem to
illustrate this.
Suppose you have a die and you want to test it to see if
it is a fair die, with equal chances of coming up with an
even number (2, 4, 6) or an odd number (1, 3, 5). You toss
the die 20 times. Using a binomial calculator such as
this
one, what is the probability that you will get exactly
ten even tosses?
How many or how few even tosses would you have to get
before you would conclude that the die was not fair?
Explain. Put this in terms of a starting hypothesis and
reasonable doubt.
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