AP Statistics Assignment

Ninth Chapter

(In Class work is in parenthesis)

Bring 25 pennies, 2 dimes, 2 nickels, 1 quarter

Pg. 568 (9.2, 9.3), 9.1, 9.4Pg. 577 (9.8, 9.10), 9.7, 9.9

Pg. 588 (9.20, 9.22), 9.19, 9.21, 9.23

Pg. 595 (9.32, 9.34), 9.31, 9.33

Pg. 601 (9.36, 9.38), 9.35, 9.39, 9.40

Ninth Chapter Vocabulary

Page

Word

598central limit theorem

593mean of a sample mean

582mean of a sample proportion

565population proportion

583rule of thumb 1

583rule of thumb 2

565sample proportion

567sampling distribution

594sampling distribution of a sample mean from a Normal Population

582sampling distribution of p-hat

593standard deviation of a sample mean

582standard deviation of a sample proportion

574unbiased

574unbiased estimator

575variability of a statistic

Quiz 9.1A

AP Statistics

Name:

An opinion poll asks, Are you afraid to go outside at night within a mile of your home because of crime? Suppose that the proportion of all adults who would say Yes to this question is p = 0.4.

1.Use the partial table of random digits below to simulate the result of an SRS of 20 adults. Be sure to explain clearly which digits you used to represent each of Yes and No. Write directly on or above the table so that I can follow the results of your simulation. What proportion of your 20 responses were Yes?

6 8 4 1 73 5 0 1 31 5 5 2 97 2 7 6 58 5 0 8 95 7 0 6 7

8 2 7 3 95 7 8 9 02 0 8 0 74 7 5 1 1 8 1 6 7 65 5 3 0 0

6 0 9 4 0 7 2 0 2 41 7 8 6 8 2 4 9 4 36 1 7 9 09 0 6 5 6

3 6 0 0 91 9 3 6 51 5 4 1 23 9 6 3 88 5 4 5 34 6 8 1 6

3 8 4 4 84 8 7 8 91 8 3 3 82 4 6 9 73 9 3 6 44 2 0 0 6

2.Repeat Question 1 using the next consecutive lines of the digits table with one line per SRS until you have simulated the results of 5 SRSs of size 20 from the same population. Compute the proportion of Yes responses in each sample. These are the values of the statistic in 5 samples. Find the mean of your 5 values of . Is it close to p?

3.The sampling distribution of is the distribution of from all possible SRSs of size 20 from this population. What is the mean of this distribution?

4.If the population proportion changed to p = 0.5, what would be the mean of the sampling distribution?

Quiz 9.1B

AP Statistics

Name:

In items 13, classify each underlined number as a parameter or statistic. Give the appropriate notation for each.

1.Forty-two percent of todays 15-year-old girls will get pregnant in their teens.

2.A 1993 survey conducted by the Richmond Times-Dispatch one week before election day asked voters which candidate for the states attorney general they would vote for. Thirty-seven percent of the respondents said they would vote for the Democratic candidate. On election day, 41% actually voted for the Democratic candidate.

3.The National Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44 years of age is 128 and the standard deviation is 15. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure for these executives is 126.07.

Below are histograms of the values taken by three sample statistics in several hundred samples from the same population. The true value of the population parameter is marked on each histogram.

4. Which statistic has the largest bias among these three? Justify your answer.

5. Which statistic has the lowest variability among these three?6. Based on the performance of the three statistics in many samples, which is preferred as an

estimate of the parameter? Why?

Quiz 9.2A

AP Statistics

Name:

Choose an SRS of size n from a large population with population proportion p having some characteristic of interest. Let be the proportion of the sample having that characteristic.

1.What is the mean of the sampling distribution?

2.What is the standard deviation of the sampling distribution?

3.Under what conditions will the formula for the standard deviation of be reasonably accurate?

4.The sampling distribution of is approximately Normal when the sample size n is large. What conditions need to be met in order to use the Normal approximation to the sampling distribution of ?

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children.

5.What is the probability that more than 20% of the sample are from poverty households? (Remember to check that you can use the Normal approximation.)

Quiz 9.2B

AP Statistics

Name:

Suppose you are going to roll a fair six-sided die 60 times and record , the proportion of times that a 1 or a 2 is showing.

1. Where should the distribution of the 60 -values be centered? Justify your answer.

2. What is the standard deviation of the sampling distribution of , the proportion of all rolls of the die that show a 1 or a 2?

3. Describe the shape of the sampling distribution of . Justify your answer.

Power companies kill trees growing near their lines to avoid power failures due to falling limbs in

storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the

chemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees.

The power company tests the chemical on 250 sycamores. Consider these an SRS from the

population of all sycamore trees.

4. What are the mean and standard deviation of the proportion of trees that are killed?

5.What is the probability that at least 60 trees (24% of the sample) are killed? (Remember to check that you can use the Normal approximation.)

Quiz 9.3A

AP Statistics

Name:

The weights of newborn children in the United States vary according to the Normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies a newborn as having low birth weight if the weight is less than 5.5 pounds.

1. What is the probability that a baby chosen at random weighs less than 5.5 pounds at birth?

You choose three babies at random and compute their mean weight, .

2. What are the mean and standard deviation of the sampling distribution of the mean weight of the three babies?

3. What is the probability that their average birth weight is less than 5.5 pounds?Quiz 9.3B

AP Statistics

Name:

The composite scores of students on the ACT college entrance examination in a recent year had a Normal distribution with mean = 20.4 and standard deviation = 5.8.

1.What is the probability that a randomly chosen student scored 24 or higher on the ACT?

2.What are the mean and standard deviation of the average ACT score for an SRS of 30 students?

3.What is the probability that the average ACT score of an SRS of 30 students is 24 or higher?

4.Would your answers to 1, 2, or 3 be affected if the distribution of ACT scores in the population were distinctly non-Normal?

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