An estimate of the population mean is . The standard error is . The distribution is       (examples: normal / t12 / chisquare4 / F5,6).

Later, when the medical devices are in full production, a consultant advised that the breaking strength of these devices should not be less than 5.5 psi (pounds per square inch) on average. In the latest batch produced, a technician has noticed a visual defect that may affect the breaking strength of the devices. To investigate, a sample of 8 devices are randomly selected from the batch and the pressure at which they break are recorded as :
6.6, 7.7, 8.0, 6.3, 6.1, 6.3, 6.3, 6.1
these are summarized as having an average breaking strength of 6.68 psi and a standard deviation of s = 0.75 psi.
Test, at significance level α = 0.05, whether there is evidence that the average breaking strength of the batch of devices is less than the required breaking strength, by testing the hypotheses:
H 0: μ = 5.5 psi
H a: μ < 5.5 psi.

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 = 0.05, the rejection region is:
(less/greater) than (2 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 breaking strength of the entire batch, μ, is less than 5.5 psi.

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 normally distributed.
Insert your choice (a or b): .