Question

uestion

Question 10 5 pts

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 95% level of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?

Group of answer choices

77.7% to 82.3%

69.2% to 86.4%

76.5% to 83.5%

78.2% to 81.8%

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 1600 / 2000 = 0.800

1 - = 1 - 0.800 = 0.2

Z/2 = 1.96

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

= 1.96 * (((0.800 * 0.2) / 2000)

Margin of error = E = 0.018

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.800 - 0.018 < p < 0.800 + 0.018

0.782 < p < 0.818

95% confidence is 78.2% to 81.8%