In a random sample of 100 residents from a certain area it follows that 35 were in favour of the construction of a nuclear power plant. Constructs a 95% confidence interval for the proportion of all residents in favour of this plant. Give the upper limit.

Answer 1

To construct a confidence interval for the proportion of all residents in favor of the construction of a nuclear power plant, we can use the formula for a confidence interval for a proportion:

Confidence Interval = (Sample Proportion) ± (Critical Value) * (Standard Error)

First, we need to calculate the sample proportion:

Sample Proportion = (Number of residents in favor of the construction) / (Sample Size)
Sample Proportion = 35 / 100
Sample Proportion = 0.35

The critical value for a 95% confidence interval can be found by using a z-table or a calculator, and it is typically approximately 1.96 for large sample sizes.

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / (Sample Size))
Standard Error = sqrt((0.35 * (1 - 0.35)) / 100)
Standard Error = sqrt(0.35 * 0.65 / 100)
Standard Error = sqrt(0.2275 / 100)
Standard Error = sqrt(0.002275)
Standard Error ≈ 0.0477

Now, we can plug the values into the formula to calculate the confidence interval:

Confidence Interval = 0.35 ± 1.96 * 0.0477

Calculating the upper limit:

Confidence Interval (Upper Limit) = 0.35 + 1.96 * 0.0477
Confidence Interval (Upper Limit) = 0.35 + 0.0937
Confidence Interval (Upper Limit) ≈ 0.443

Therefore, the upper limit of the 95% confidence interval for the proportion of all residents in favor of the construction of a nuclear power plant is approximately 0.443.