In a recent poll, 260 people were asked if they liked dogs, and 8% said they did. Find the margin of error of this poll, at the 90% confidence level.
Give your answer to three decimals
To find the margin of error, we need to use the formula:
Margin of Error = Critical Value * Standard Error
First, we need to calculate the critical value, which corresponds to the desired confidence level. For a 90% confidence level, we can find the critical value using a standard normal distribution table or a calculator. The critical value for a 90% confidence level is 1.645.
Next, we need to calculate the standard error. The standard error is the standard deviation divided by the square root of the sample size. Since the poll result is expressed as a percentage (8%), we need to convert it to a decimal (0.08) before calculating the standard error.
Standard Deviation = sqrt(p * (1 - p) / n)
Standard Error = sqrt(0.08 * (1 - 0.08) / 260)
Calculating the standard error:
Standard Deviation = sqrt(0.08 * 0.92 / 260)
= sqrt(0.00736 / 260)
= sqrt(0.0000283)
= 0.005316
Finally, we can calculate the margin of error:
Margin of Error = 1.645 * 0.005316
= 0.008737
Rounded to three decimals, the margin of error for this poll at the 90% confidence level is 0.009.