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AP Statistics Name___________________________________________________Show work for any calculations as well as provide reasons for ALL answers.

1. The histograms below represent the distribution of five different data sets, eachcontaining 28 integers, from 1 through 7, inclusive. The horizontal and vertical scalesare the same for all graphs. Which graph represents the data set with the largeststandard deviation?

2. The histogram below represents data obtained after the censusof an entire population was conducted.

The sampling distribution of thesample mean based on samples ofsize 2 for the population was

simulated, and a histogram of the results wasproduced. Which of the following histograms is mostlikely the histogram of that sampling distribution?

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3. The graphs of the sampling distribution, I and II, of the sample mean of the samerandom variable for samples of two different sizes are shown above. Which of thefollowing must be true about the sample sizes?

(a) The sample size of I is less than the sample size of II.(b) The sample size of I is greater than the sample size of II.(c) The sample size of I is equal to the sample size of II.(d) The sample size does not affect the sampling distribution.(e) The sample sizes cannot be compared based on these graphs.

4. Five estimators for a parameter are being evaluated. The true value of theparameter is 0. Simulations of 100 random samples, each of size n, are drawn from

the population. For each simulated sample, the five estimators are computed. Thehistograms below display the simulated sampling distributions for the five estimators.Which simulated sampling distribution is associated with the best estimator for thisparameter?

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USE THE FOLLOWING TO ANSWER QUESTIONS 5 & 6:Every Thursday, Matt and Daves Video Venture has roll-the-dice day. A customermay choose to roll two fair dice and rent a second movie for an amount (in cents) equalto the numbers uppermost on the dice with the larger number first. For example, if thecustomer rolls a two and a four, a second movie may be rented for $0.42. If a two and atwo are rolled, a second movie may be rented for $0.22. Let X represent the amountpaid for a second movie on roll-the-dice day. The expected value of X is $0.47 and thestandard deviation of X is $0.15.

5.If a customer rolls the dice and rents a second movie every Thursday for 20consecutive weeks, what is the total amount that the customer would expect to payfor these second movies?

(a) $0.45(b) $0.47(c) $0.67(d) $3.00(e) $9.40

6. If a customer rolls the dice and rents a second movie every Thursday for 30consecutive weeks, what is the approximate probability that the total amount paid forthese second movies will exceed $15.00?

(a) 0(b) 0.09(c) 0.14(d) 0.86(e) 0.91

7. The population {2, 3, 5, 7} has = 4.25 and = 1.92. When sampling withreplacement, there are 16 different possible samples of size 2 that can be selectedfrom this population. The mean of each of these 16 samples is computed. Forexample, 1 of the 16 samples is (2,5) which has a mean of 3.5. The distribution of

the 16 sample means has its own mean x and its own standard deviation x . Which

of the following statements is true?

(a) x = 4.25 and x = 1.92

(b) x = 4.25 and x > 1.92

(c) x = 4.25 and x < 1.92

(d)x

> 4.25(e) x < 4.25

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8. A recent survey concluded that the proportion of American teenagers who have a cellphone is 0.27. The true population proportion of American teenagers who have a cellphone is 0.29. For sample size 1,000 that are selected at random from thispopulation, what are the mean and standard deviation, respectively, for the samplingdistribution of the sample proportion of American teenagers who have a cell phone?

(a) 0.27, )73.0)(27.0(1000

(b) 0.27,1000

)71.0)(29.0(

(c) 0.27,1000

)73.0)(27.0(

(d) 0.29,1000

)71.0)(29.0(

(e) 0.29, )71.0)(29.0(1000

9. Julie generates a sample of 20 random integers between 0 and 9 inclusive. Sherecords the number of 6s in the sample. She repeats this process 99 more times,

recording the number of 6s in each sample. What kind of distribution has shesimulated?

(a) The sampling distribution of the sample proportion with n = 20 and p = 0.6(b) The sampling distribution of the sample proportion with n = 100 and p = 0.1(c) The binomial distribution with n = 20 and p = 0.1(d) The binomial distribution with n = 100 and p = 0.1(e) The binomial distribution with n = 20 and p = 0.6

10. Suppose that public opinion in a large city is 65 percent in favor of increasing taxesto support the public school system and 35 percent against such an increase. If a

random sample of 500 people from this city are interviewed, what is theapproximate probability that more than 200 of these people will be againstincreasing taxes?

(a)300200 )35.0()65.0(

200

500

(b)300200 )65.0()35.0(

200

500

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(c)

500

)35.0)(65.0(

65.040.0 >z

(d)

500

)6.0)(4.0(

35.040.0 >z

(e)500

)65.0)(35.0(

35.040.0 >z

ANSWERS: D, C, B, B, E, C, C, D, C, E