Question

At a canning facility, a technician is testing a machine that is supposed to deliver 250 milliliters of product. The technician tests 44 samples and determines the volume of each sample. The 44 samples have a mean volume of 251.6 mL. The machine is out of calibration when the average volume it dispenses differs significantly from 250 mL.
The technician wants to perform a hypothesis test to determine whether the machine is out of calibration. Assume standard deviation = 5.4 is known. Compute the value of the test statistic.


Potential answers are:


4.57


0.30


13.04


0.24


1.97

Answer 1

Answer:

1.97

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 250$

The alternate hypotesis is:

$H_{1} \neq 250$

Our test statistic is:

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

In which X is the sample mean, $\mu$ is the hypothesis tested(null hypothesis), $\sigma$ is the standard deviation and n is the size of the sample.

In this problem, we have that:

$X = 251.6, \mu = 250, \sigma = 5.4, n = 44$

So

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

$t = \frac{251.6 - 250}{\frac{5.4}{\sqrt{44}}}$

$t = 1.97$