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Contact [7]
3 years ago
6

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 σ = 5.4 is known. Compute the value of the test statistic.
Mathematics
1 answer:
Serhud [2]3 years ago
4 0

Answer:

The value of the test statistic is t = 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 null hypothesis value, \sigma is the standard deviation and n is the size of the sample.

In this problem:

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

The value of the test statistic is t = 1.97

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