Question

a market research firm is hired to estimate the percentage of adults living in a large city who have cell phones. Five hundred randomly selected adults are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes-they own cell phones which interval below is closest to the 95% confidence interval.

Answer 1

Solution :

Given that,

n = 421

x = 500

Point estimate = sample proportion = = x / n = 421 / 500 = 0.842

1 - = 1 - 0.842 = 0.158

At 95% confidence level ,

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 ((( 0.842 * 0.158 ) / 500 )

= 0.032

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.842 - 0.032 < p < 0.842 + 0.032

0.810 < p < 0.874

81.0% < p < 87.4%

The 95% confidence interval for the population proportion p is : - 81.0% < p < 87.4%