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Answer:
i) There is insufficient evidence to support the claim that the standard deviation of the instruments is less than 0.00002 millimeters.
ii)
Step-by-step explanation:
represent the sample standard deviation
represent the significance level for the test
represent the value that we want to test
n=8 represent the sample size
A chi-square test can be used to test "if the standard deviation of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test".
Null and alternatve hypothesis
The system of hypothesis on this case would be given by:
Null Hypothesis:
Alternative Hypothesis:
The statistic to test this is given by:
(1)
Part i) Calculate the statistic
If we replace into formula (1) we got this:
(1)
The critical region for a for a lower one-tailed alternative is given by
The degrees of freedom are given by
And if we use the Chi Square distribution with 7 degrees of freedom we see that
And our critical region would be so on this case we can conclude that we fail to reject the null hypothesis. So it's not enough evidence to conclude that the population standard deviation is less than 0.00002 mm.
Part ii) Calculate the p value
In order to calculate the p value we can do this:
If we compare this value with the significance level (0.01) we see that
This agrees with the conclusion since when the p values is greater than the significance level we FAIL to reject the null hypothesis, same conclusion as part i).