Question

Exhibit 9-2 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 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The test statistic is _____. a. .056 b. 1.96 x. 2.00 d. 1.64

Answer 1

Answer:

c. 2.00

Step-by-step explanation:

The value of the test statistic is the value of t, given by

$t = \frac{\overline{x} - \mu_{0}}{\frac{s}{\sqrt{n}}}$

In which $\overline{x}$ is the mean of our sample, $\mu_{0}$ is the mean we are testing, $s$ is the standard deviation of the sample and $n$ is the size of the sample.

In this problem, we have that:

$\overline{x} = 3.1, \mu_{0} = 3, s = 0.5, n = 100$

So

$t = \frac{\overline{x} - \mu_{0}}{\frac{s}{\sqrt{n}}}$

$t = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}} = \frac{0.1}{0.05} = 2$

So the correct answer is:

c. 2.00