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

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In a poll of 1000 randomly selected voters in a local election, 728 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

In a poll of 1000 randomly selected voters in a local election, 728 voters were against school bond measures.

So, the sample proportion is: 728/1000 = 0.728 (p-hat, say)

We know that margin of error = Critical value x Standard error of the sample.

Here, the formula of margin of error will be: z* ((p-hat*(1-p-hat))/n)^0.5

z denotes the critical value, which is 1.96 here (95% confidence interval)

((p-hat*(1-p-hat))/n)^0.5 = (0.728*0.272 / 1000)^0.5 = (0.000198^0.5) ] = 0.0141

0.0141*1.96 = 0.0276

This is value of the margin of error.