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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

1 Answer

3 votes

Answer:

1.97

Explanation:

The null hypothesis is:


H_(0) = 250

The alternate hypotesis is:


H_(1) \\eq 250

Our test statistic is:


t = (X - \mu)/((\sigma)/(√(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 = (X - \mu)/((\sigma)/(√(n)))


t = (251.6 - 250)/((5.4)/(√(44)))


t = 1.97

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