Question

When the medical devices are in full production, a consultant advised that the breaking strength of these devices should not be less than 5.6 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 11 devices are randomly selected from the batch and the pressure at which they break are recorded as : 6.0, 5.7, 5.8, 5.7, 5.8, 6.1, 5.5, 6.3, 6.0, 5.3, 5.8 these are summarized as having an average breaking strength of 5.82 psi and a standard deviation of s = 0.28 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 = 5.6 psi H a: μ < 5.6 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 5.6 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): .

Answer 1

The standard error is =0.084

The distribution is t11

The test statistic has value TS= 2.606

Testing at significance level α = 0.05, the rejection region is: less than -1.81 Since the test statistic is in the rejection region, there (is evidence to reject the null hypothesis Ho

There is sufficient evidence to suggest that the average breaking strength of the entire batch, μ, is less than 5.6 psi.

b: Yes - the population distribution must be normally distributed.