Question

The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. Refer to Exhibit 8-2. If the confidence coefficient is reduced to .80, the standard error of the mean _____.

Answer 1

The standard error of the mean remains unchanged.

Explanation:

Given that:

The standard error (S.E) of the mean
`= (\sigma)/(√(n))` with is independent of confidence coefficient.

The margin of error
`E = z * S.E`

This explains the claim that as the confidence coefficient reduces, the z-value also reduces, so as the Margin of error (E) but the standard error will always remain unchanged.

i.e.

From the question;

sample size n = 100

standard deviation = 1

mean = 3.0

The standard error (S.E) of the mean
`= (1)/(√(100))`

= 0.1

So, if the confidence coefficient is reduced to 0.80, the standard error of the mean remains unchanged.