A national polling company randomly selected 275 eligible voters and asked them which presidential candidate they supported. 110 voters responded that they supported candidate A. Find the 95% confidence interval for the sample proportion that support candidate A. Use z=1.960. Round to the nearest tenth of a percent

To find the 95% confidence interval for the sample proportion, we can follow these steps:

Step 1: Calculate the sample proportion.
The sample proportion is calculated by dividing the number of voters who support candidate A (110) by the total number of voters in the sample (275):

Sample proportion (p̂) = Number of voters supporting candidate A / Total number of voters
= 110 / 275
= 0.4

Step 2: Calculate the standard error.
The standard error represents the estimated standard deviation of the sample proportion. It can be calculated using the formula:

Standard error (SE) = √(p̂(1 - p̂) / n)

Where:
p̂ is the sample proportion
n is the sample size

SE = √(0.4(1 - 0.4) / 275)

SE ≈ 0.026

Step 3: Calculate the margin of error.
The margin of error is a measure of the uncertainty in the sample proportion. It can be calculated by multiplying the standard error by the critical value. In this case, the critical value is z=1.960 (corresponding to a confidence level of 95%):

Margin of error = z * SE
= 1.960 * 0.026
≈ 0.051

Step 4: Determine the confidence interval.
The confidence interval is calculated by subtracting and adding the margin of error from the sample proportion:

Lower bound = p̂ - Margin of error
= 0.4 - 0.051
≈ 0.349

Upper bound = p̂ + Margin of error
= 0.4 + 0.051
≈ 0.451

So, the 95% confidence interval for the sample proportion that support candidate A is approximately 34.9% to 45.1%. Rounded to the nearest tenth of a percent, the confidence interval is 35% to 45%.