1.

The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population ofxvalues has an approximately normal distribution.

1222 1306 1187 1299 1268 1316 1275 1317 1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean yearxand sample standard deviations. (Round your answers to the nearest whole number.)

x=______A.D.

s=___________yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)lower limit______A.D.

upper limit ___________-A.D.

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2.

A poll asked the question, "What do you think is the most important problem facing this country today?"Seventeenpercent of the respondents answered "crime and violence." The margin of sampling error was plus or minus2percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.

lower limit_______%

upper limit ________%

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3.

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of0.1in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate forpis0.21

____________

(b) there is no preliminary estimate forp

____________

___________________________

4)

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of66professional actors, it was found that41were extroverts.

(a) Letprepresent the proportion of all actors who are extroverts. Find a point estimate forp. (Round your answer to four decimal places.)

___________

(b) Find a 95% confidence interval forp. (Round your answers to two decimal places.)

lower limit________

upper limit ________

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

(c) Do you think the conditionsnp>5 andnq>5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.

_____________________

5.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of5300permanent dwellings on an entire reservation showed that1669were traditional hogans.

(a) Letpbe the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate forp. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval forp. (Round your answer to three decimal places.)

lower limit _________

upper limit___________

Give a brief interpretation of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.

99% of the confidence intervals created using this method would include the true proportion of traditional hogans.

1% of all confidence intervals would include the true proportion of traditional hogans.

99% of all confidence intervals would include the true proportion of traditional hogans.

(c) Do you think thatnp>5 andnq>5 are satisfied for this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.