Question

The Consumer Reports National Research Center conducted a telephone survey of 2,000 adults to learn about the major economic concerns for the future. The survey results showed that 1,700 of the respondents think the future health of Social Security is a major economic concern. If computing the confidence intervals manually, make sure to use at least three decimal digits for the critical values.

B. At 90% confidence, what is the margin of error (to 4 decimals)?

Answer 1

Solution :

Given that,

n = 2000

x = 1700

Point estimate = sample proportion = = x / n = 1700/2000=0.85

1 - = 1-0.85=0.15

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 (((0.85*0.15) /2000 )

= 0.013