Question

In a random sample of 27 people, the mean commute time to work was 3044 minules and the standard deviation was 7.1 minutes. Assume the population is normaly distributed and use a t-distribution to construct a 90% confidence interval for the population mean μ. What is the margin of error of μ ? laterpret the resulte The confidence interval for the population mean μ is (Round to one decimal place as needed.) The margin of error of μ is (Round to one decimal place as needed.) Interpret the results.

A) With 90% confidence, it can be said that the commule time is between the bounds of the confidence interval
B) If a large sample of people are taken approximately 90% of them will have commute fimes between the bounds of the confidence interval.
C) With 90% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.
D) It can be said that 90% of people have a commute time between the bounds of the confidance intevral.

Answer 1

To construct a 90% confidence interval for the population mean μ, we use the formula (x - EBM, x + EBM), where x is the sample mean and EBM is the margin of error. The margin of error for this sample is 1.949 minutes, resulting in a confidence interval of (3042.05, 3045.95) for the population mean μ.

Step-by-step explanation:

To construct a 90% confidence interval for the population mean μ, we can use the formula:

(x - EBM, x + EBM)

Where x is the sample mean and EBM is the error bound or margin of error. The formula for EBM is:

EBM = (t-value) * (standard deviation / sqrt(sample size))

In this case, the sample mean is 3044 minutes, the standard deviation is 7.1 minutes, and the sample size is 27. Since we are using a t-distribution, we need to find the t-value. With a 90% confidence level and a sample size of 27, the degrees of freedom is 26. Looking up the t-value in a t-table, we find that the t-value is approximately 1.708. Plugging in the values into the formula:

EBM = 1.708 * (7.1 / sqrt(27)) = 1.949

So the margin of error is 1.949 minutes. The confidence interval for the population mean μ is (3044 - 1.949, 3044 + 1.949), which simplifies to (3042.05, 3045.95).