At a water bottling facility, a technician is testing a bottle filling machine that is supposed...

At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 500 milliliters of water. The technician dispenses 38 samples of water and determines the volume of each sample. The 38 samples have a mean volume of . The machine is out of calibration if the mean volume differs from . Use the p-value method.

The technician wants to perform a hypothesis test to determine whether the machine is out of calibration. The standard deviation of the dispensed volume is known to be

i). State the appropriate null and alternate hypotheses.
ii). Compute the value of the test statistic.
iii). State a conclusion. Use the level of significance.

Solutions

Expert Solution

The given question misses values of sample mean volume , the machine is out of calibration if the mean volume differs from and standard deviation of dispensed volume is known to be..

Dear , I have assumed the following values for your question, Your satisfaction is more important to me that is why I didn't skipped this question..

sample mean volume differs from= 498.3 ml

the machine is out of calibration if the mean volume differs from 500 ml

standard deviation of dispensed volume is known to be 7.5

If the above assumed values are true then please carry out the below statistical test...

Null hypothesis : population mean = 500ml

Alternative hypothesis : population mean not equal to 500 ml

ii )

We can use one sampe normal test here since sample size = 38 which is greater than 30 and population standard deviation is known.

Test statistic = (498.3 - 500)/(7.5/✓38) = -3.82657

iii. ) P value = 0.00012 < level of significance (0.1 or 0.05 or 0.01).

There fore we reject null hypothesis.

We conclude that the machine is out of calibration

orchestra answered 1 year ago

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