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### 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 give-or-take 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 give-or-take 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 z-score 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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