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1. Student: _____________________ Date: _____________________ Instructor: Doug Ensley Course: MAT117 01 Applied Statistics - Ensley Assignment: Online 10 - Section 7.1 Consider a sampling distribution with and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion. p = 0.12 a. For a random sample of size . n = 5000 b. For a random sample of size . n = 1000 c. For a random sample of size . n = 500 a. The mean is . The standard deviation is . (Round to four decimal places as needed.) b. The mean is . The standard deviation is . (Round to four decimal places as needed.) c. The mean is . The standard deviation is . (Round to four decimal places as needed.) Summarize the effect of the sample size on the size of the standard deviation. A. As the sample size gets larger, the standard deviation gets smaller. B. As the sample size gets smaller, the standard deviation gets smaller. C. Standard deviation does not depend on the size of the sample. Online 10 - Section 7.1-Doug Ensley https://xlitemprod.pearsoncmg.com/api/v1/print/math 1 of 5 9/30/15, 4:50 PM

Online 10 - Section 7.1-Doug Ensleywebspace.ship.edu/deensley/m117/onlineHW/Online 10 - Section 7.1... · Assignment: Online 10 - Section 7.1 ... Using the appropriate formulas,

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1.

Student: _____________________Date: _____________________

Instructor: Doug EnsleyCourse: MAT117 01 Applied Statistics -Ensley

Assignment: Online 10 - Section 7.1

Consider a sampling distribution with and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion.

p = 0.12

a. For a random sample of size . n = 5000b. For a random sample of size .n = 1000c. For a random sample of size .n = 500

a. The mean is .

The standard deviation is . (Round to four decimal places as needed.)

b. The mean is .

The standard deviation is . (Round to four decimal places as needed.)

c. The mean is .

The standard deviation is . (Round to four decimal places as needed.)

Summarize the effect of the sample size on the size of the standard deviation.

A. As the sample size gets larger, the standard deviation gets smaller.B. As the sample size gets smaller, the standard deviation gets smaller.C. Standard deviation does not depend on the size of the sample.

Online 10 - Section 7.1-Doug Ensley https://xlitemprod.pearsoncmg.com/api/v1/print/math

1 of 5 9/30/15, 4:50 PM

2.

3.

For the population of people who suffer occasionally from migraine headaches, suppose is the proportion who get some relief from taking a certain medicine. For a particular subject, let x 1 if they get relief and x 0 if they do not. For a random sample of people who suffer from migraines, answer the following questions.

p = 0.40= =

38

a. State the probability distribution for each observation. Choose the sentence below that best describes the probability distribution.

A. For each random sample of people, about get some relief from taking the medicine and do not.

38 1523

B. For each observation, the probability that the medicine helps is and the probability that it does not help is .

0.400.60

C. For each random sample of people, about get some relief from taking the medicine and do not.

38 2315

D. For each observation, the probability that the medicine helps is and the probability that it does not help is .

0.600.40

b. Find the mean of the sampling distribution of the sample proportion who get relief.

mean (Round to two decimal places as needed.)=

c. Find the standard deviation of the sampling distribution of the sample proportion.

standard deviation (Round to four decimal places as needed.)=

d. Explain what the standard deviation in part (c) describes. Choose the sentence below that best describes the standard deviation.

A. the standard deviation of the population distributionB. the standard deviation of the sampling distributionC. the probability that the sample mean equals the population meanD. the difference between the sample mean and the population mean

In an exit poll, suppose that the mean of the sampling distribution of the proportion of the people in the sample who voted for recall was and the standard deviation was . Answer the following questions.

31300.65 0.0085

a. Based on the approximate normality of the sampling distribution, give an interval of values within which the sample proportion will almost certainly fall. Choose the correct interval below.

A. to 0.642 0.659B. to − 0.009 0.009C. to − 0.026 0.026D. to 0.625 0.676

b. Based on the result in (a), if you take an exit poll and observe a sample proportion of , would this be a rather unusualresult? Why?

0.66

A. , because the observed sample proportion lies the interval.No outsideB. , because the observed sample proportion lies the interval.Yes outsideC. , because the observed sample proportion lies the interval.Yes withinD. , because the observed sample proportion lies the interval.No within

Online 10 - Section 7.1-Doug Ensley https://xlitemprod.pearsoncmg.com/api/v1/print/math

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4. A baseball player in the major leagues who plays regularly will have about at bats (that is, about times he can be the hitter in a game) during a season. Suppose a player has a probability of getting a hit in an at-bat. His batting average at the end of the season is the number of hits divided by the number of at-bats. This batting average is a sampleproportion, so it has a sampling distribution describing where it is likely to fall. Complete parts a and b below.

600 6000.338

a. Describe the shape, mean, and standard deviation of the sampling distribution of the player's batting average after a season of at-bats.600

Describe the shape of the sampling distribution. Choose the correct response below.

A. The distribution is bell-shaped, centered on a standard deviation of , and has a minimum value of 0 and a maximum value of one mean value.

0.019

B. The distribution is bell-shaped, centered on a standard deviation of , and the majority of the distribution lies within three mean values of the standard deviation.

0.019

C. The distribution is bell-shaped, centered on a mean of , and the majority of the distribution lies within three standard deviations of the mean.

0.338

D. The distribution is bell-shaped, centered on a mean of , and has a minimum value of 0 and a maximum value of one standard deviation.

0.338

b. Explain why a batting average of or would not be especially unusual for this player's year-end batting average.

0.319 0.357

A. Year-end batting averages of and lie one standard deviation from the mean.Therefore, it is not unlikely that a player with a career batting average of would have ayear-end batting average of or .

0.357 0.3190.338

0.357 0.319B. Year-end batting averages of and lie three standard deviations from the mean.

Therefore it is almost a certainty that the player will recieve a year-end batting average between and .

0.357 0.319

0.357 0.319C. Year-end batting averages of and lie three standard deviations from the mean.

Therefore it is extremely unlikely that the player will recieve a year-end batting average of or .

0.357 0.319

0.357 0.319

Online 10 - Section 7.1-Doug Ensley https://xlitemprod.pearsoncmg.com/api/v1/print/math

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5. The figure illustrates two sampling distributions for sample proportions when the population proportion p . Complete parts a through c.= 0.55

a. Find the standard deviation for the sampling distribution of the sample proportion with (i) n = 200, (ii) n = 2000.

(i) standard deviation =

(ii) standard deviation =(Round to four decimal places as needed.)

b. Explain why the sample proportion would be very likely to fall (i) between and when n , and

and when 0.44 0.66 = 200

(ii) between 0.52 0.58 n = 2000.

A. The sample proportion has to be between 0 and 1.

B. The sample proportion is very likely to equal the population proportion when n is larger.

C. The sample proportion has to be close to the population proportion.

D. The sample proportion is very likely to fall within three standard deviations of the mean.

c. Explain how the results in (b) indicate that the sample proportion is closer to the population proportion when the sample size is larger.

A. When n is larger, the standard deviation is smaller, so the interval is larger.

B. When n is larger, the standard deviation is smaller, so the interval is smaller.

C. When n is larger, the standard deviation is larger, so the interval is smaller.

D. When n is larger, the standard deviation is larger, so the interval is larger.

0.4 0.5 0.6 0.7

x

n = 2000

n = 200

Online 10 - Section 7.1-Doug Ensley https://xlitemprod.pearsoncmg.com/api/v1/print/math

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1. 0.12

0.0046

0.12

0.0103

0.12

0.0145

A. As the sample size gets larger, the standard deviation gets smaller.

2. B.For each observation, the probability that the medicine helps is and the probability that it does not help is .0.40 0.60

0.40

0.0795

B. the standard deviation of the sampling distribution

3. D. to 0.625 0.676

D. , because the observed sample proportion lies the interval.No within

4. C.The distribution is bell-shaped, centered on a mean of , and the majority of the distribution lies within three standard deviations of the mean.

0.338

A.Year-end batting averages of and lie one standard deviation from the mean. Therefore, it is not unlikely that a player with a career batting average of would have a year-end batting average of or .

0.357 0.3190.338 0.357 0.319

5. 0.0352

0.0111

D. The sample proportion is very likely to fall within three standard deviations of the mean.

B. When n is larger, the standard deviation is smaller, so the interval is smaller.

Online 10 - Section 7.1-Doug Ensley https://xlitemprod.pearsoncmg.com/api/v1/print/math

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