Directions: Work on these sheets. Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers? (a) 72% is a sample; 56% is a population (b) 72% and 56% are both statistics (c) 72% is a statistic statistic and 56% is a parameter (d) 72% is a parameter and 56% is a statistic (e) 72% and 56% are both parameters
ho urs a light bulb burns before failing varies from bulb to bulb. T he distribution of 2. The number of hours burnout times is strongly skewed skewed to the right. The central limit theorem says that (a) as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type. (b) the average burnout time of any number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. (c) the average burnout time of any number of bulbs has a distribution that is close to Normal. (d) the average burnout time of a large number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. (e) the average burnout time of a large number of bulbs has a distribution that is close to Normal. 3. The Gallup Poll has decided to increase the size of its random random sample of Canadian Canadian voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of Canadian voters who favor a new law banning smoking in public buildings. The effect of this increase is to (a) reduce the bias of the estimate. estimate. (b) increase the bias of the estimate. (c) reduce the variability of the estimate. (d) increase the variability of the estimate. (e) have no effect since the population size is the same. 4. Which of the following statements about the sampling distribution of the sample mean is INCORRECT: (a) The standard deviation of the sampling distribution will decrease decrease as the sample size increases. (b) The standard deviation of the th e sampling distribution is a measure of the variability of the sample mean among repeated samples. (c) The sample mean is an unbiased estimator of the true (unknown) population mean. (d) The sampling distribution shows how the sample mean will vary among repeated samples. (e) The sampling distribution shows how the sample was distributed distributed around the sample mean.
Chapter 9
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Test 9D
5. Suppose we select an SRS of size n = 100 from a large population having proportion p proportion p of of successes. Let p be the proportion of successes successes in the sample. For which value of p of p would would it be safe to use ˆ
Normal approximation to the sampling distribution of (a) 0.01 (b) 1/11 (c) 0.85
p ˆ
? (d) 0.975
(e) 0.999
6. A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, wi with th the additional revenue revenue going to education. Let p denote the proportion in the sample who say they support the increase. Suppose that 40% ofall of all adults in Ohio support the increase. The standard deviation of p is (a) 0.40 (b) 0.24 (c) 0.0126 (d) 0.00016 (e) 0 ˆ
ˆ
7. Suppose we are planning on taking an SRS of size n from a population. If we double the sample size, then x will be multiplied by
(a) 2 (b) (e) none of these
1
2
Part 2: Free Response
(c) 2
(d) 1/2
Communicate your thinking clearly and completely. completely.
Poll of a random sample of 1089 Canadians (total population of 30,000,000) found that 8. A Gallup Poll about 80% favored capital punishment. A Gallup Poll of a random sample of o f 1089 Americans (total population of 300,000,000) also found that 80% favored capital capital punishment. Theaccuracy The accuracy of an estimate describes the closeness of that e stimate to the unknown true parameter value. Precision is Precision is the degree to which repeated repeate d estimates produced using the same sampling method would provide answers very close to each other. (a) Which poll gives a more accurate estimate of the proportion of that nation’s citizens who favor capital punishment? Justify your answer.
(b) Which poll gives a more precise more precise estimate of the proportion of that nation’s citizens who favor capital punishment? Justify your answer.
Chapter 9
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Test 9D
interested in the demographics of those those who listen to the radio programs programs they 9. Companies are interested sponsor. A radio station has determined that only 20% of listeners phonin g in to a morning talk program are male. The station management wonders if adding a male host to the program will increase the proportion of callers callers who are male. After adding the the male host, the station records the gender of 200 people who phone in to the program during a particular week. week. The station is willing to view these 200 callers ca llers as an SRS from the population of all a ll those who call in to this program. For the moment, assume that the addition of the male host has no effect on the proportion of callers who are male. (a) If p is the proportion of callers in the sample who a re male, what is the mean of the sampling ˆ
distribution of
p ˆ
?
(b) What is the standard deviation of the sampling distribution of p ? ˆ
(c) Explain why you can use the formula formula for the standard deviation of p in this setting. ˆ
(d) In fact, during this particular week, 50 of the the 200 callers were male. Does this provide sufficient evidence to suggest suggest that the proportion of male callers callers has increased from 20%? To answer this question, calculate the probability of obtaining a sample of 200 callers in which still p = 0.20. p 0.25 if the true population proportion of callers to the show who are male is still p Be sure to check that you can use the Normal approximation. ˆ
(e) Based on your answer to part (d), can the station management conclude that the addition of the male host caused an increase in the proportion proportion of male callers to the program? Explain.
Chapter 9
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Test 9D
10. The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 65 grams (g) and standard deviation 5 g.
(a) Calculate the probability that a randomly selected egg weighs between 62.5 g and 68.75 g. Show your work.
Think of cartons of such eggs as SRSs of size 12 from the population of all eggs. (b) Calculate the probability that the mean weight of a carton falls between 62.5 g and 68.75 g. Show your work.
(c) Did you need to know that the population pop ulation distribution of egg weights was Normal in order to complete parts (a) or (b)? Justify your your answer.
Bonus: Suppose Bonus: Suppose you obtain a carton of eggs that is supposed to be from this type of hen, and only two of the eggs weigh weigh between 62.5 g and 68.75 g. What would you conclude about whether the eggs came from this type type of hen? Give appropriate statistical statistical evidence to support your your answer.
I pledge that I have neither given nor received aid on this test. ___________________________ Chapter 9
