You are to test the claim by a mineral water bottle manufacturer that its bottles contain an average of 1000 ml (1 litre). A random sample of n = 12 bottles resulted in the measurements (in ml): 992, 1002, 1000, 1001, 998, 999, 1000, 995, 1003, 1001, 997 and 997.
It is assumed that the true variance of water in all bottles is ?² = 1.5, and that the amount of water in bottles is normally distributed.
Test the manufacturer's claim at the 1% significance level (you may use Excel to calculate the p-value). Also, briefly comment on what the hypothesis test result means about the manufacturer's claim, and if an error might have occurred which type of error it would be.
In summary, the assignment requires:
• the calculation of the sample mean from the raw observations
• the formulation of the hypotheses, [Math Processing Error] and [Math Processing Error]
• calculation of the test statistic value
• calculation of the $$p$-value$
• a decision of whether or not to reject [Math Processing Error]
• an inferential conclusion about what the test result means
• indication of which type of error might have occurred.
