An automatic bottling machine fills oil into 2-liter (2,000 cm3) bottles. A consumer advocate wants to...

An automatic bottling machine fills oil into 2-liter (2,000 cm³) bottles. A consumer advocate wants to test the null hypothesis that the average amount filled by the machine into a bottle is at least 2,000 cm³. A random sample of 40 bottles coming out of the machine was selected and the exact contents of the selected bottles are recorded. The sample mean was 1,999.6 cm ³. The population standard deviation is known from past experience to be 1.30 cm³.

Test the null hypothesis at α of 5%.
Assume that the population is normally distributed with the same standard deviation of 1.30 cm³. Assume that the sample size is only 20 but the sample mean is the same 1,999.6 cm³. Conduct the test once again at α of 5%.
If there is a difference in the two test results, explain the reason for the difference

Solutions

Expert Solution

(a)

(b)

(c)

Yes, in part a we reject the null hypothesis while in part b we fail to reject the null hypothesis.

Reason: As the sample size decreases standard error increase and test statistics decreases. So chances to reject the null hypothesis also decreases.

orchestra answered 1 year ago

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