The volume of “one liter” flasks used in laboratories varies about a mean value

Question

The volume of “one liter” flasks used in laboratories varies about a mean value that is controlled by a machine that prints the markings on the flask. Assume that the volumes of flasks produced by the machine are approximately normally distributed. A sample of 75 flasks gave a mean volume at the one liter mark on the flask of 1.04 liters and a standard deviation of 0.11 liters. Does the data present sufficient evidence to conclude that the mean volume at the one liter mark is not exactly one liter as claimed by the manufacturer?

a) Define the random variable and its assumed probability distribution.

b) Test an appropriate set of hypotheses to address the question of interest by calculating a p-value and interpreting its numerical value in the context of the problem.

c) If your decision in part (b) was an mistake, what type of error did you commit?

Explanation / Answer

a. A variable is any characteristics, number, or quantity that can be measured or counted. Volume is random variable here and its distribution is normal

b. We need to test H0: mu=1 liter vs H1: mu not equal to 1

As it is normally ditributed with n=75>30 we will use z statistics

z=xbar-mu/(sd/sqrt(n))=3.15

The P-Value is 0.001633.

pvalue<alpha(0.05) we reject null hypothesis

c. In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").

So if b was mistake i would have made type 1 error.

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