Question

You are given the samples mean and the population standard deviation, Use this information to construct 90% and 95% confidence intervals for population mean interprit the results and compare the width of the confidence interval. If convenient, use technology to construct the confidence interval.

A random sample of 50 home theatre systems has a mean price of $12300, Assume population standard deviation $15.60.Find 90% confidence interval.

Answer 1

To construct a 90% confidence interval for the population mean, use the formula (x - EBM, x + EBM), where x is the sample mean and EBM is the error bound for a population mean. Given a sample mean of $12300 and a population standard deviation of $15.60 for a random sample of 50 home theater systems, the 90% confidence interval is ($12296.46, $12303.54).

Step-by-step explanation:

To construct a 90% confidence interval for the population mean, we will use the formula (x - EBM, x + EBM), where x is the sample mean and EBM is the error bound for a population mean. Given that the sample mean is $12300 and the population standard deviation is $15.60, we need to calculate the EBM. The formula for EBM is (z * (σ / √n)), where z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size. Since the confidence level is 90%, the z-score is 1.645. Plugging in the values, we get EBM = 1.645 * (15.60 / √50). Calculating this, we find that EBM ≈ $3.54.

Therefore, the 90% confidence interval for the population mean is ($12300 - $3.54, $12300 + $3.54), which simplifies to ($12296.46, $12303.54).