in mm: 3.2, 2.8, 2.7, 3.0, 2.9, 2.9, 2.9, 3.2, 2.8 these gave an average of 2.93 mm and the widths varied by a standard deviation of s = 0.17 mm. Test, at significance level α = 0.01, whether there is evidence that the average bond width of the batch of devices is different to the required specification, by testing the following hypotheses: H 0: μ = 3 mm H a: μ ≠ 3 mm. Complete the test by filling in the blanks in the following:
A company that manufactures medical devices is conducting tests in R&D on a new product. The product is in production on a pilot run (product will not be sold from the pilot run). The product is manufactured in batches and the quality of the batch must be determined, by testing a sample of 9 devices selected at random from a batch. One aspect that is monitored is the width of the bond in the device, ideally this should be equal to 3 mm on average.
A sample from the latest batch gave the following bond widths measured in mm:
3.2, 2.8, 2.7, 3.0, 2.9, 2.9, 2.9, 3.2, 2.8
these gave an average of 2.93 mm and the widths varied by a standard deviation of s = 0.17 mm.
Test, at significance level α = 0.01, whether there is evidence that the average bond width of the batch of devices is different to the required specification, by testing the following hypotheses:
H 0: μ = 3 mm
H a: μ ≠ 3 mm.
Complete the test by filling in the blanks in the following:
An estimate of the population mean is .
The standard error is .
The distribution is (examples: normal / t12 / chisquare4 / F5,6).
The test statistic has value TS= .
Testing at significance level α = 0.01, the rejection region is:
less than and greater than (3 dec places).
Since the test statistic (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H 0.
There (is sufficient/is insufficient) evidence to suggest that the average bond width of the entire batch of devices, μ, is different to 3 mm.
Were any assumptions required in order for this inference to be valid?
a: No - the Central Limit Theorem applies, which states the sampling distribution is normal for any population distribution.
b: Yes - the population distribution must be
Insert your choice (a or b): .
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