Question

Critical values for quick reference during this activity. Confidence level Critical value 0.90 z∗=1.645 0.95 z∗=1.960 0.99 z∗=2.576 Jump to level 1 In a poll of 1000 randomly selected voters in a local election, 403 voters were against school bond measures. What is the sample proportion p^? (Should be a decimal answer) What is the margin of error m for the 95% confidence level? (Should be a decimal answer)

Answer 1

The sample proportion p^ can be calculated by dividing the number of voters against school bond measures by the total number of voters:

p^ = 403/1000 = 0.403

The margin of error m for the 95% confidence level can be calculated using the formula:

m = z*(sqrt(p^*(1-p^)/n))

Where:
- z* is the critical value for the confidence level (given as 1.960 for 95% confidence level)
- p^ is the sample proportion
- n is the sample size

Substituting the values, we get:

m = 1.960*(sqrt(0.403*(1-0.403)/1000)) = 0.032

Therefore, the sample proportion p^ is 0.403 and the margin of error m for the 95% confidence level is 0.032.