Question

A sample of 427 phone calls directed by a local telephone company has a mean duration time of 11.33 minutes. Assuming that σ = 4.4 minutes, find the margin of error in estimating μ at the 95% level of confidence.

Answer 1

To find the margin of error in estimating the population mean (μ) with a 95% level of confidence, use the formula: Margin of Error = Critical Value * Standard Error. Plug in the given values to calculate the margin of error.

Step-by-step explanation:

To find the margin of error in estimating the population mean (μ) at a 95% level of confidence, we can use the formula:

Margin of Error = Critical Value * Standard Error

First, we need to find the critical value. Since we are estimating μ at a 95% level of confidence, the critical value is the z-score corresponding to a 95% confidence level. From the z-table, the z-score for a 95% confidence level is approximately 1.96.

Next, we need to calculate the standard error. The formula for the standard error is: Standard Error = σ / sqrt(n), where σ is the population standard deviation and n is the sample size. In this case, σ = 4.4 minutes and n = 427.

Plugging in the values, we get:

Standard Error = 4.4 / sqrt(427)

Finally, we can calculate the margin of error:

Margin of Error = 1.96 * (4.4 / sqrt(427))

Solving this equation, we find that the margin of error is approximately 0.44 minutes.