# For this problem, carry at least four digits after the decimal

11.

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 of 70 professional actors, it was found that 45 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (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 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.

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

(c) Do you think the conditions n·p > 5 and n·q > 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 that p̂ is approximately binomial.

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

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

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

12.

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

In a marketing survey, a random sample of 996 supermarket shoppers revealed that 272 always stock up on an item when they find that item at a real bargain price.

(a) Let p represent the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain. Find a point estimate for p. (Enter a number. Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (For each answer, enter a number. Round your answers to three decimal places.)

lower limit

upper limit

Give a brief explanation of the meaning of the interval.

5% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

5% of all confidence intervals would include the true proportion of shoppers who stock up on bargains.

95% of all confidence intervals would include the true proportion of shoppers who stock up on bargains.

95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

(c) As a news writer, how would you report the survey results on the percentage of supermarket shoppers who stock up on items when they find the item is a real bargain?

Report p̂ along with the margin of error.

Report the margin of error.

Report the confidence interval.

Report p̂.

What is the margin of error based on a 95% confidence interval? (Enter a number. Round your answer to three decimal places.)

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