Question

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.
a. 1.457
b. 2.333
c. 1.848
d. 2.037

Answer 1

Answer:

b. 2.333

Step-by-step explanation:

Test if the mean transaction time exceeds 60 seconds.

At the null hypothesis, we test if the mean transaction time is of 60 seconds, that is:

$H_0: \mu = 60$

At the alternate hypothesis, we test if it exceeds, that is:

$H_1: \mu > 60$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

60 is tested at the null hypothesis:

This means that $\mu = 60$

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.

This means that $n = 16, X = 67, s = 12$

Value of the test statistic:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{67 - 60}{\frac{12}{\sqrt{16}}}$

$t = \frac{7}{3}$

$t = 2.333$

Thus, the correct answer is given by option b.