Question

A shop has recently introduced a new system, which aims to reduce clients’ waiting time below 6 minutes. After several months that the new system has been operating, the management wishes to study whether the new system is effective. A sample of 100 shop customer waiting times is collected. The average and the standard deviation of this sample are 5.5 minutes and 2.4 minutes respectively.

Calculate a 95% confidence interval for ?, the mean of all possible shop clients waiting times using the new system.

Are we 95% confident that ? is less than 6 minutes?

Answer 1

95% confidence interval for $\mu$ is

$\bar{x}$ - t * S / sqrt(n) < $\mu$ < $\bar{x}$ + t * S / sqrt(n)

5.5 - 1.984 * 2.4 / sqrt(100) < $\mu$ < 5.5 + 1.984 * 2.4 / sqrt(100)

5.024 < $\mu$ < 5.976

95% CI for $\mu$ is ( 5.024 , 5.976)

Since mean of 6 is not contained in this interval, we have sufficient evidence to

support claim.

We are 95% confident that $\mu$ is less than 6 minutes.