(1) For this problem, carry at least fourdigits after the decimal in your calculations. Answers may varyslightly due to rounding.
In a random sample of 65 professional actors, it was found that37 were extroverts.
(a) Let p represent the proportion ofall 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 ____
(2) For this problem, carry at least fourdigits after the decimal in your calculations. Answers may varyslightly due to rounding.
Santa Fe black-on-white is a type of pottery commonly found atarchaeological excavations at a certain monument. At one excavationsite a sample of 610 potsherds was found, of which 365 wereidentified as Santa Fe black-on-white.
(a) Let p represent the proportion ofSanta Fe black-on-white potsherds at the excavation site. Find apoint estimate for p. (Round your answer to four decimalplaces.) ____
(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 fora 95% confidence interval to have a maximal margin of error of 0.1in the following scenarios? (Round your answers up the nearestwhole number.)
(a) a preliminary estimate for p is0.34 ____
(b) there is no preliminary estimate for p____
