(a) Consider140binomial trials with44successes.

Find a 90% confidence interval for the population proportion of successesp. (Round your answers to three decimal places.)

• lower limit
• upper limit

(b) Consider234binomial trials with70successes.

Find a 95% confidence interval for the population proportion of successesp. (Round your answers to three decimal places.)

• lower limit
• upper limit

(c) What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of0.1

• 1. if a preliminary estimate forpis0.24?

minimum sample size=

• 2. if there is no preliminary estimate forp?

minimum sample size=

(d) What is the minimal sample size needed for a 99% confidence interval to have a maximal margin of error of0.1

• 1. if a preliminary estimate forpis0.71?

minimum sample size=

• 2. if there is no preliminary estimate forp?

minimum sample size+