Question

Previous Page Next Page Question 5 (7 points) A survey of 450 citizens found that 351 of them favor a new bill.introdu city. We want to find a 95% confidence interval for the true proportion of th who favor the bill. What is the lower limit of the interval? (Round to 3 decimal digits) Your Answer: Answer View hint for Quoctin

Answer 1

Solution:

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

x = 351

n = 450

P = x/n = 351/450 = 0.78

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.78± 1.96* sqrt(0.78*(1 – 0.78)/450)

Confidence Interval = 0.78 ± 1.96* 0.0195

Confidence Interval = 0.78 ± 0.0383

Lower limit = 0.78 - 0.0383 = 0.7417

Answer: 0.742