Question

The average time, in minutes, a person spends online before purchasing music is normally distributed with a population standard deviation of 4 minutes and an unknown population mean. If a random sample of 18 shoppers is taken and results in a sample mean of 32 minutes, find the error bound (EBM) of the confidence interval with a 90% confidence level.

Answer 1

To find the error bound (EBM) of the confidence interval with a 90% confidence level, we can use the formula: EBM = 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.

Step-by-step explanation:

To find the error bound (EBM) of the confidence interval with a 90% confidence level, we can use the formula: EBM = 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.

In this case, we have a 90% confidence level, so the corresponding z-score can be found using a standard normal distribution table. The z-score for a 90% confidence level is approximately 1.645.

Plugging in the values into the formula, we get: EBM = 1.645 * (4 / √18) ≈ 1.535. Therefore, the error bound of the confidence interval is approximately 1.535 minutes.