EXAM PREPAP Statisticsname:Date

EXAM PREPAP StatisticsName:Date:

Directions: Work on these sheets. A standard normal table is attached.

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1.In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

(a) 95

(b) 85.5

(d) 95.5

(e) None of the above

2.Refer to the previous problem. On the final exam Carla scored 98. What is the value of her residual?

(a) 98

(b) 2.5

(d) 0

(e) None of the above

3.A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). A least squares line was fit to the data. Here is the residual plot from this least squares fit.

What does the pattern of the residuals tell you about the linear model?

(a) The evidence is inconclusive.

(b) The residual plot confirms the linearity of the fuel economy data.

(d) The residual plot clearly contradicts the linearity of the data.

(e) None of the above

4. All but one of the following statements contains a blunder. Which statement is correct?

(a) There is a correlation of 0.54 between the position a football player plays and their weight.

(b)The correlation between planting rate and yield of corn was found to be r=0.23.

(c)The correlation between the gas mileage of a car and its weight is r=0.71 MPG.

(d)We found a high correlation (r=1.09) between the height and age of children.

(e)We found a correlation of r=–.63 between gender and political party preference.

5. You measure the age, marital status and earned income of an SRS of 1463 women. The number and type of variables you have measured is

(a)1463; all quantitative.

(b)four; two categorical and two quantitative.

(c)four; one categorical and three quantitative.

(d)three; two categorical and one quantitative.

(e)three; one categorical and two quantitative.

6. A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct?

(a)Your friend must not have followed the diet correctly, since she did not lose weight.

(b)Since your friend did not lose weight, the report must not be correct.

(c)The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend’s experience does not necessarily contradict the study results.

(d)In order for the study to be correct, we must now add your friend’s results to those of the study and recompute the new average.

(e)Your friend is an outlier.

7. “Normal” body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5° C with a standard deviation of 0.3° C. When converted to °F, the mean and standard deviation are

(°F = °C(1.8) + 32).

(a)97.7, 32

(b)97.7, 0.30

(d)97.7, 0.97

(e)97.7, 1.80

8. The following is a histogram showing the actual frequency of the closing prices on the

New York exchange of a particular stock. Based on the frequency histogram for New York Stock exchange, the class that contains the 80th percentile is:

(a)20-30

(b)10-20

(d)50-60

(e)30-40

9.There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the

(a)mean age will stay the same but the variance will increase.

(b)mean age will stay the same but the variance will decrease.

(c)mean age and variance will stay the same.

(d)mean age and variance will increase.

(e)mean age and variance will decrease.

10.The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Half of all young men are shorter than

(a)65.5 inches

(b) 68 inches

(d) can't tell, because the median height is not given

(e) none of the above

11.Use the information in the previous problem. Only about 5% of young men have heights outside the range

(a) 65.5 inches to 70.5 inches

(b) 63 inches to 73 inches

(d) 58 inches to 78 inches

(e) none of the above

12. For the density curve shown to the right,

which statement is true?

(a)The density curve is symmetric.

(b)The density curve is skewed right.

(c)The area under the curve between 0 and 1 is 1.

(d)The density curve is normal.

(e)None of the above is correct.

13.For the density curve shown in question 3, which statement is true?

(a)The mean and median are equal.

(b)The mean is greater than the median.

(c)The mean is less than the median.

(d)The mean could be either greater than or less than the median.

(e)None is the above is correct

14.For the density curve shown, what is the mean?

(a)0

(b)0.25

(d)0.75

(e)None of the above

15.A smooth curve which approximates the shape of a histogram and describes the overall pattern of a distribution is called

(a)a stemplot

(b)a normal plot

(c)a normal probability plot

(d)a density curve

(e)none of the above

16.A normal density curve has which of the following properties?

(a)It is symmetric.

(b)It has a peak centered above its mean.

(c)The spread of the curve is proportional to it standard deviation.

(d)All of the properties, (a) to (c), are correct.

(e)None of the properties, (a) to (c), is correct.

17.The area under the standard normal curve corresponding to –0.3<Z<1.6 is

(a)0.3273

(b)0.4713

(d)0.9542

(e)None of the above

18.What do we call a sample that consists of the entire population?

(a)A stratum

(b)A multistage sample

(c)A mistake. A sample can never be the entire population.

(d)A census

(e)None of the above.

19.A member of Congress wants to know what his constituents think of proposed legislation on health insurance. His staff reports that 228 letters have been received on the subject, of which 193 oppose the legislation. What is the population in this situation?

(a)The constituents

(b)The 228 letters received

(c)The 193 opposing the legislation

(d)Congress

(e)None of the above.

20.Which of the following is a method for improving the accuracy of a sample?

(a)Use no more than 3 or 4 words in any question

(b)When possible, avoid the use of human interviewers, relying on computerized dialing instead

(c)Use large sample sizes

(d)Use smaller sample sizes

(e)None of the above.
21.We say that the design of a study is biased if which of the following is true?

(a)A racial or sexual preference is suspected

(b)Random placebos have been used

(c)Certain outcomes are systematically favored

(d)The correlation is greater than 1 or less than –1

(e)None of the above.

22.Control groups are used in experiments in order to . . .

(a)Control the effects of lurking variables such as the placebo effect

(b)Control the subjects of a study so as to insure all participate equally

(c)Guarantee that someone other than the investigators, who have a vested interest in the outcome, control how the experiment is conducted

(d)Achieve a proper and uniform level of randomization

(e)None of the above.

23.A randomly selected student is asked to respond to yes, no, or maybe to the question, “Do you intend to vote in the next presidential election?” The sample space is { yes, no, maybe }. Which of the following represent a legitimate assignment of probabilities for this sample space?

(a)0.4, 0.4, 0.2

(b)0.4, 0.6, 0.4

(d)0.5, 0.3, –0.2

(e)None of the above

24.You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have a probability of .6 of winning. The probability that you win the next two matches is

(a)0.16

(b)0.36

(d)0.6

(e)1.2

25.If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?

(a)0.1248

(b)0.28

(d)0.76

(e)The answer cannot be determined from the information given

26.Suppose X is a random variable with mean µ. Suppose we observe X many times and keep track of the average of the observed values. The law of large numbers says that

(a)The value of µ will get larger and larger as we observe X.

(b)As we observe X more and more, this average and the value of µ will get larger and larger.

(c)This average will get closer and closer to µ as we observe X more and more often.

(d)As we observe X more and more, this average will get to be a larger and larger multiple of µ.

(e)None of the above

27.In a population of students, the number of calculators owned is a random variable X with P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2. The mean of this probability distribution is

(a)0

(b)2

(d)0.5

(e)The answer cannot be computed from the information given.

28.Refer to the previous problem. The variance of this probability distribution is

(a)1

(b)0.63

(d)0.4

(e)The answer cannot be computed from the information given.

29.The weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. What is the probability that the next report will weigh less than 45g?

(a)0.1042

(b)0.1056

(d)0.0418

(e)The answer cannot be computed from the information given.

30.In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is

(a) 0.3020

(b) 0.2634

(d) 0.5

(e)1

(f)None of the above

31.In a certain large population, 40% of households have a total annual income of $70,000. A simple random sample of 4 of these households is selected. What is the probability that 2 or more of the households in the survey have an annual income of over $70,000?

(a) 0.3456

(b)0.4000

(d)0.5248

(e)The answer cannot be computed from the information given.

32.A factory makes silicon chips for use in computers. It is known that about 90% of the chips meets specifications. Every hour a sample of 18 chips is selected at random for testing. Assume a binomial distribution is valid. Suppose we collect a large number of these samples of 18 chips and determine the number meeting specifications in each sample. What is the approximate mean of the number of chips meeting specifications?

(a) 16.20

(b)1.62

(d)16.00

(e)The answer cannot be computed from the information given.

33.Which of the following are true statements?

I.The expected value of a geometric random variable is determined by the formula (1 – p)n–1p.

II.If X is a geometric random variable and the probability of success is .85, then the probability distribution of X will be skewed left, since 85 is closer to 1 than to 0.

III.An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting.

(a) I only

(b)II only

(c)III only

(d)I, II, and III

(e)None of the above gives the complete set of true responses.

34.Following a dramatic drop of 500 points in the Dow Jones Industrial Average in September 1998, a poll conducted for the Associated Press found that 92% of those polled said that a year from now their family financial situation will be as good as it is today or better. The number 92% is a

(a)Statistic

(b)Sample

(c)Parameter

(d)Population

(e)None of the above.

35.If a population has a standard deviation , then the standard deviation of the mean of 100 randomly selected items from this population is

(a)

(b)100

(c)/10

(d)/100

(e)0.1

36.The distribution of values taken by a statistic in all possible samples of the same size from the same population is

(a)The probability that the statistic is obtained

(b)The population parameter

(c)The variance of the values

(d)The sampling distribution of the statistic

(e)None of the above.

37. If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal

to the true value of the parameter being estimated, the statistic is said to be

(a)Random

(b)Biased

(d)Unbiased

(e) None of the above.

38.You want to compute a 96% confidence interval for a population mean. Assume that the population standard deviation is known to be 10 and the sample size is 50. The value of z* to be used in this calculation is

(a)1.960

(b) 1.645

(d)2.0537

(e)None of the above.

39.A simple random sample of 1000 Americans found that 61% were satisfied with the service provided by the dealer from which they bought their car. A simple random sample of 1000 Canadians found that 58% were satisfied with the service provided by the dealer from which they bought their car. The sampling variability associated with these statistics is

(a)Exactly the same.

(b)Smaller for the sample of Canadians because the population of Canada is smaller than that of the United States, hence the sample is a larger proportion of the population.

(c)Smaller for the sample of Canadians because the percentage satisfied was smaller than that for the Americans.

(d)Larger for the Canadians because Canadian citizens are more widely dispersed throughout the country than in the United States, hence they have more variable views.

(e)About the same.

40.You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is  = 100. If you want the margin of error to be approximately 10, you will need a sample size of

(a) 16

(b) 271

(d) 1476

(e) None of the above.

41.A significance test was performed to test the null hypothesis H0: µ = 2 versus the alternative Ha: µ 2. The test statistic is z = 1.40. The P-value for this test is approximately

(a)0.16

(b)0.08

(d)0.92

(e)0.70

(f) None of the above.

42. To determine the reliability of experts used in interpreting the results of polygraph examinations in criminal investigations, 280 cases were studied. The results were:

True Status

Innocent Guilty

Examiner’s “Innocent” 131 15

Decision “Guilty” 9 125

If the hypotheses were H0: suspect is innocent vs. Ha: suspect is guilty, then we could estimate the probability of making a Type II error as:

(a)15/280

(b)9/280

(d)9/140

(e)15/146

43.In preparing to use a t procedure, suppose we were not sure if the population was normal. In which of the following circumstances would we not be safe using a t procedure?

(a)A stemplot of the data is roughly bell shaped.

(b)A histogram of the data shows moderate skewness.

(c)A stemplot of the data has a large outlier.

(d)The sample standard deviation is large.

(e)The t procedures are robust, so it is always safe.

44.The weights of 9 men have mean = 175 pounds and standard deviation s = 15 pounds. What is the standard error of the mean?

(a)58.3

(b)19.4

(d)1.7

(e)None of the above.

45.What is the critical value t* that satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*?

(a)1.397

(b)1.282

(d) 0.90

(e)None of the above.

46.Suppose we have two SRSs from two distinct populations and the samples are independent. We measure the same variable for both samples. Suppose both populations of the values of these variables are normally distributed but the means and standard deviations are unknown. For purposes of comparing the two means, we use

(a)Two-sample t procedures

(b)Matched pairs t procedures

(c)z procedures

(d)The least-squares regression line

(e)None of the above.

47.Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are normally distributed with mean . A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0: = 14, Ha: < 14.

To do this, he selects sixteen bags of this brand at random and determines the net weight of each. He finds the sample mean to be = 13.82 and the sample standard deviation to be s = 0.24.

We conclude that we would

(a)Reject H0 at significance level 0.10 but not at 0.05.

(b)Reject H0 at significance level 0.05 but not at 0.025.

(c)Reject H0 at significance level 0.025 but not at 0.01.

(d)Reject H0 at significance level 0.01.

(e)Fail to reject H0 at the = 0.10 level.

48. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately

(a)0.03

(b)0.25

(d)6.12

(e)0.06

(f)None of the above.

49.An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are:

(a)

(b)

(c)

(d)

(e)None of the above.

50.A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out he poses the following question to his listeners. “Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?” He asks listeners to phone in and vote “yes” if they agree the drinking age should be lowered and “no” if not. Of the 100 people who phoned in 70 answered “yes.” Which of the following conditions for inference about a proportion using a confidence interval are violated?

(a)The data are an SRS from the population of interest.

(b)The population is at least ten times as large as the sample.

(c)n is so large that both the count of successes n p and the count of failures n(1 – p) are ten or more.

(d)There appear to be no violations.

(e)More than one condition is violated.

Total Time spent working on test______hours

Chapter 3 1Test 3A