Question

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly different than 3 minutes. Use α = 0.05.

A) The test statistic is ___________.
i. 1.96
ii. 1.64
iii. 2.00
iv. 0.056

Answer 1

iii. 2.00

Explanation:

Our test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the population mean(the mean we are testing),
`\sigma` is the standard deviation and n is the size of the sample.

We are testing a mean of 3 times.

This means that
`\mu = 3`

The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. Sample of 100.

So
`X = 3.1, \sigma = 0.5, n = 100`

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (3.1 - 3)/((0.5)/(√(100)))`

`t = 2`

So the correct answer is:

iii. 2.00