A researcher wishes to estimate with 90 confidnce the propo

A researcher wishes to estimate , with 90% confidnce, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 1% of the true proportion.

a. fnd the minimum sample size needed, using prior study that found that 36% of the respondents said they have high-speed Internet access.

b. No preliminary estimate is available. Find the minimum sample size needed.

Solution

Confidence level is 90% hence z score = 1.64

Let sample size be n

Margin of error = 1.64(se)

SE^2 = 0.36(0.64)/n

SE = 0.48/rtn

1.64( 0.48/rtn)<0.01

rtn>78.72

n >6197