# Stat multiple choice questions

Question

4

Multiple Choice (3 points each)

Write the best answer on the ANSWER SHEET

1) Federal guidelines require that pharmaceutical companies provide evidence that a new drug is

effective by demonstrating that two independently conducted randomized studies both show

statistically significant benefit from the drug at significance level of 0.025, i.e. ? = 0.025. Given

that the null hypothesis is that the drug has no benefit, what type of error has been committed if a

new drug appears beneficial to the FDA when in fact the drug provides no benefit?

a) Type I error

b) Type II error

c) No error was made

2) Consider the following probability distribution:

If the mean for this probability distribution is 12, what is c?

a) 4

b) 6

c) 8

d) 10

e) 12

3) In a study of 82 young ?under the age of 32? drivers, 39 were men who were ticketed, 11 were

men who were not ticketed, 8 were women who were ticketed, and 24 were women who were not

ticketed ?based on data from the Department of Transportation?. If one of these subjects is

randomly selected, find the probability of getting a man or someone who was ticketed.

a) 0.707

b) 0.805

c) 0.122

d) 0.476

e) 0.207

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4) The Beardstown Bearcats baseball team plays 60 percent of its games at night and 40 percent in

the daytime. It wins 55 percent of its night games but only 35 percent of its day games. You read

in the paper that the Bearcats won their last game against the Manteno Maulers. What is the

probability that it was played at night?

a) 0.486

b) 0.057

c) 0.702

d) 0.131

e) 0.227

5) In a recent Gallup poll on a random sample of 1,028 US adults, 11% said they approve of the way

the Congress is handling its job, with a 95% confidence interval of 7% to 15%. Which of the

following statements is/are true based on the confidence interval?

(i) The population proportion is 0.11.

(ii) The sample proportion is 0.11.

(iii) The margin of error is 0.04.

(iv) 95% of random samples will have sample proportions between 0.07 and 0.15.

(v) It is possible that the population proportion is 0.18.

a) They all are true

b) None of them are true

c) (i), (iii) and (iv) are true

d) (ii), (iv) and (v) are true

e) (ii), (iii) and (v) are true

f) None of the above

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Is sleep necessary? To investigate, researchers measured the activity patterns of breeding sandpipers (a

type of bird) in the high Arctic in summer, when the sun never sets. The accompanying figure shows the

observed percent time that individual males were awake and active in a 2008 field study. The data are on

the left. To the right of the data are the sample mean (filled circle) and error bars for the standard

deviation, the standard error of the mean, and a 95% confidence interval for the mean in no particular

order.

6) Which of the error bars indicates the standard deviation?

a) A

b) B

c) C

7) Which error bar indicates the standard error of the mean?

a) A

b) B

c) C

8) Which error bar indicates a 95% confidence interval for the mean?

a) A

b) B

c) C

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9) In the following standard normal curve, suppose that the total shaded area is 0.2302. What is x?

a) 1.2

b) 2.4

c) 0.74

d) 0.26

e) 1.57

10) The probability that a football team wins a game is 0.48. Given that the team played 16 games in

the regular season, what is the variance of the number of games this football team wins in a

season?

a) 1

b) 2

c) 3

d) 4

e) 5

11) 40 randomly chosen people were asked whether they like fish; 13 said yes. Find a 95%

confidence interval for ?, the proportion of people in the whole population who like fish.

a) (0.18,0.47)

b) (0.26, 0.39)

c) (0.15,0.50)

d) (0.13 0.52)

e) (0.21 0.43)

12) An economist is interested in studying the incomes of consumers in a particular country. A

random sample of 50 individuals resulted in a mean income of $15,000 and a standard deviation

of $1000. What is the width of the 95% confidence interval for the mean?

a) $232.60

b) $364.40

c) $465.23

d) $554.37

e) $418.20

8

13) The mean of the sampling distribution of the sample mean is:

a) equal to the mean of the population.

b) an approximation of the mean of the population.

c) not a good estimate of the population mean.

d) equal to the population mean divided by n.

e) none of the above.

14) Suppose that the height of adult ostriches is normally distributed with a mean µ = 2.3 meters and

a standard deviation ? = 0.2 meters. If an adult ostrich is chosen at random, what is the

probability that it is less than 2 meters tall?

a) 0.053

b) 0.36

c) 0.58

d) 0.067

e) 0.104

15) For the continuous uniform probability density function sketched below, what is the probability

that the random variable X is between 2 and 4.5?

a) 0.375

b) 0.500

c) 0.625

d) 1.000

e) Cannot be determined

16) An unbiased estimate

a) has mean equal to the true parameter.

b) is equal to the true parameter

c) has the smallest variance of all possible estimates

d) none of the above

e) all of the above

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17) You want to design a study to estimate the proportion of students on your campus who agree with

the statement, “The student government is an effective organization for expressing the needs of

students to the administration.” You will use a 95% confidence interval and you would like the

margin of error to be 0.05 or less. The minimum sample size required is approximately

a) 22

b) 1795

c) 385

d) 271

e) 543

18) A building inspector believes that the percentage of new construction with serious code violations

may be even greater than the previously claimed 7%. She conducts a hypothesis test on 200 new

homes and finds 23 with serious code violations. What is the value of her test statistic for testing

: .07 : .07 H H o a ? ? = > ?

a) 1.99

b) 1.05

c) 2.92

d) 2.49

e) 0.73

19) Which of the following statements are true?

i. It is helpful to examine your data before deciding whether to use a one-sided or a

two-sided hypothesis test.

ii. The alternative hypothesis can have an equal sign in it.

iii. The larger the p-value, the more evidence there is against the null hypothesis.

a) I only

b) II only

c) III only

d) II and III

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

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20) Why is the central limit theorem important in statistics?

a) Because for a large sample size n, it says the sampling distribution of the sample

mean is approximately normal, regardless of the shape of the population.

b) Because for a large sample size n, it says the population is approximately normal.

c) Because for any population, it says the sampling distribution of the sample mean

is approximately normal, regardless of the shape of the population.

d) Because for any sample size n, it says the sampling distribution of the sample

mean is approximately normal.

21) Consider a multiple regression analysis attempting to predict the value of a home from several

variables. One variable of interest is the location of the home. If homes can be located in either a

rural, urban, or suburban area, how many dummy variables would we need to include in this

model in order to account for the location of a home?

a) 4

b) 3

c) 2

d) 1

22) In a given data set the larger the R2

a) The lower the SSE

b) The larger the SSE

c) The lower the SSR

23) Cook’s distance measure is used to

a) identify influential observations in multiple regression analysis.

b) determine the significance of an independent variable.

c) determine if there is significant multicollinearity.

d) determine if the overall regression model is significant.

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The economic structure of Major League Baseball allows some teams to make substantially more money

than others, which in tur n allows some teams to spend much more on player salaries. These teams might

therefore be expected to have better players and win more games on the field as a result. Suppose that

after collecting data on team payroll (in millions of dollars) and season win total for 2010, we find a

regression equation of Wins = 71.87 + 0.101Payroll – 0.060League where League is an indicator variable

that equals 0 if the team plays in the National League or 1 if the team plays in the American League.

24) If Teams A and B both play in the same league, and Team A’s payroll is $1 million higher than

Team B’s, then we would expect Team A to win, on average,

a) 0.101 games more than Team B.

b) 71.87 games more than Team B.

c) 0.060 games more than Team B.

d) 0.060 games fewer than Team B.

25) If Teams A and B have the same payroll, but Team A plays in the National League while Team B

plays in the American League, then we would expect Team A to win, on average,

a) 0.101 games more than Team B.

b) 71.87 games more than Team B.

c) 0.060 games more than Team B.

d) 0.060 games fewer than Team B.

26) Suppose we plotted the data and drew the regression lines for National League and American

League teams. What would be the intercept of the line for American League teams?

a) –0.060

b) 0.060

c) 0.941

d) 0.101

e) 71.81

27) Calculate the predicted number of wins for a National League team with a payroll of $98 million.

a) 65.99

b) 77.75

c) 77.85

d) 41.71

e) 81.77

28) One American League team in the data set had a payroll of $108 million and won 88 games.

Calculate the residual for this observation.

a) –1.26

b) 5.28

c) 9.65

d) 11.70

e) 22.61

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29) A multiple regression analysis was conducted for a dependent variable y on 100 independent

variables x1, x2, …, x100. Among other things, R2

was computed to be 0.87. What is the most

appropriate way to interpret this?

a) 87 of the independent variables in the model are capable of accurately predicting y.

b) We will accurately predict y 87% of the time.

c) 87 of the independent variables are statistically significant, while the remaining 13

variables should be removed from the model.

d) 87% of the variation in the observed values y can be explained by the independent

variables

30) The following interactions between dummy and continuous variables are possible, with the

exception of

a) 123 ( ) Y X D XD i o i i ii i =+ + + ?? ? ? ? × +

b) 1 2 ( ) Y X XD i o i ii i =+ + ?? ? ? × +

c) 1 ( ) Y DX i o i ii =++ + ? ??

d) Y XD i o i ii =+ + + ?? ? ? 1 2

31) Based on a random sample of 1200 adults, a 95% confidence interval for the proportion of all

adults who regularly wear a wrist watch is (0.29, 0.35). Which of the following gives the best

interpretation of this confidence interval?

a) We are 95% confident that the sample proportion of adults who regularly wear a wrist

watch is between 0.29 and 0.35.

b) We are 95% confident that the proportion of all adults who regularly wear a wrist watch

is between 0.29 and 0.35.

c) Approximately 95% of all possible samples of 1200 adults will result in a sample

proportion of adults who regularly wear a wrist watch between 0.29 and 0.35

d) There is a 95% probability that the proportion of all adults who regularly wear a wrist

watch is between 0.29 and 0.35.

32) Suppose on any given day during the winter at Jackson Hole, there is a 40% chance there is over

6’’ of fresh snow, 50% chance that there is 1’’ to 6’’ of fresh snow, and 10% chance that there is

less than 1” of fresh snow. Furthermore, given that there is over 6” of fresh snow there is a 90%

chance I snowboard, given that there is 1”- 6” of fresh snow there is a 70% chance I snowboard,

and given that there is less than 1” of fresh snow there is a 30% chance that I snowboard. Find

the probability that there is over 6” of snow given that I went snowboarding.

a) 0.486

b) 0.057

c) 0.628

d) 0.131

e) 0.227

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33) Respondents who had a tree during the holiday season were asked whether the tree was natural or

artificial. Respondents were also asked if they lived in an urban area or in a rural area. Of the 421

households displaying a Christmas tree, 160 lived in rural areas and 261 were urban residents.

The tree growers want to know if there is a difference in preference for natural trees versus

artificial trees between urban and rural households, against a two sided alternative. The tree

growers found that 68 of the rural households prefer a natural tree and 89 of the urban households

prefer a natural tree.

. prtesti 160 68 261 89,count

Two-sample test of proportions x: Number of obs = 160

y: Number of obs = 261

——————————————————————————

Variable | Mean Std. Err. z P>|z| [95% Conf. Interval]

————-+—————————————————————-

x | .425 .0390812 .3484022 .5015978

y | .3409962 .0293426 .2834857 .3985066

————-+—————————————————————-

diff | .0840038 .0488706 -.0117807 .1797884

| under Ho: .0485546 1.73 0.084

——————————————————————————

diff = prop(x) – prop(y) z = 1.7301

Ho: diff = 0

Ha: diff 0

Pr(Z < z) = 0.9582 Pr(|Z| z) = 0.0418

Does the Stata output above provide evidence that a difference exists in the preferences of rural

and urban residents?

a) Reject Ho and accept Ha

b) Fail to reject Ho

c) Accept Ho

d) Not enough information

34) Suppose the stock of Company A, a tech startup, has an expected return of .24 next year, with a

standard deviation of .12. The stock of Company B, a tire manufacturer, has an expected return of

.08, with a standard deviation of .05. The covariance between stocks A and B is .000675. What is

the correlation between stocks A and B?

a) 0.5732

b) .1125

c) .4961

d) .0986

e) .7471

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A June 2013 Gallup poll asked US residents about their opinion on sales taxes on internet purchases. The

results of the poll are summarized in the table below. The text of the survey question is also provided

above the table.

35) One of the values on the table is 73% (marked). Which of the following best describes this

probability?

a) P(Against)

b) P(18 to 29 years)

c) P(18 to 29 years | Against)

d) P(Against | 18 to 29 years)

e) P(Against and 18 to 29 years)

36) Based on these results, opinion on sales taxes on internet purchases and age appear to be

a) dependent

b) independent

c) disjoint

d) mutually exclusive

e) complementary

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