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(1) For this problem, carry at least four digits after the decimal in your calculations. Answers...

(1) 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 65 professional actors, it was found that 37 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 ____

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

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 610 potsherds was found, of which 365 were identified as Santa Fe black-on-white.

(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. 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 three decimal places.)

lower limit    
upper limit    

(3) What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.34 ____


(b) there is no preliminary estimate for p ____

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