Question
In a recent poll, 470 people were asked if they liked dogs, and 57% said they did. Find the margin of error of this poll, at the 99% confidence level.
Answers
GPT 3.5
To find the margin of error, we first need to find the standard error of the proportion.
The formula for the standard error of the proportion is:
SE = sqrt((p * (1-p)) / n)
where p is the proportion of people who said they liked dogs, and n is the sample size.
First, we need to convert the percentage into a proportion.
p = 57% / 100% = 0.57
Next, we can substitute the values into the formula:
SE = sqrt((0.57 * (1-0.57)) / 470)
Calculating this:
SE = sqrt((0.57 * 0.43) / 470)
= sqrt(0.2451 / 470)
= sqrt(0.00052)
= 0.0228
Finally, to calculate the margin of error, we need to multiply the standard error by the critical value.
At the 99% confidence level, the critical value is 2.576.
Margin of Error = 2.576 * 0.0228
= 0.0589
Therefore, the margin of error of this poll at the 99% confidence level is approximately 0.0589.
The formula for the standard error of the proportion is:
SE = sqrt((p * (1-p)) / n)
where p is the proportion of people who said they liked dogs, and n is the sample size.
First, we need to convert the percentage into a proportion.
p = 57% / 100% = 0.57
Next, we can substitute the values into the formula:
SE = sqrt((0.57 * (1-0.57)) / 470)
Calculating this:
SE = sqrt((0.57 * 0.43) / 470)
= sqrt(0.2451 / 470)
= sqrt(0.00052)
= 0.0228
Finally, to calculate the margin of error, we need to multiply the standard error by the critical value.
At the 99% confidence level, the critical value is 2.576.
Margin of Error = 2.576 * 0.0228
= 0.0589
Therefore, the margin of error of this poll at the 99% confidence level is approximately 0.0589.