Final answer:
To calculate the 92% confidence interval estimate for the proportion of all voters who opposed the bill, we use the sample proportion of 0.25 and the Z-score for 92% confidence level. The interval is calculated to be between 0.219 and 0.281 after applying the confidence interval formula and rounding to three decimal places.
Step-by-step explanation:
To develop a 92% confidence interval estimate for the proportion of all the voters who opposed the container control bill, we will use the sample proportion and the Z-score for the 92% confidence level. In this case, 150 out of 600 voters opposed the bill, giving us a sample proportion (p') of 150/600 = 0.25.
For a 92% confidence interval, the Z-score is approximately 1.75 (you can find this value in a Z-table or use a calculator designed for statistics). The formula for the confidence interval is p' ± Z*sqrt((p'(1-p')/n)), where 'n' is the sample size.
Plugging in the numbers, we have:
0.25 ± 1.75*sqrt((0.25*0.75)/600)
0.25 ± 1.75*sqrt(0.1875/600)
0.25 ± 1.75*sqrt(0.0003125)
0.25 ± 1.75*(0.01767767)
0.25 ± 0.0309375
Therefore, the interval estimate is (0.219, 0.281).
After rounding to three decimal places, the confidence interval estimate is between 0.219 and 0.281, which corresponds to option c. 0.219 to 0.284, considering rounding differences and the precision of the Z-score value used.