A bottled water distributor wants to determine whether the mean amount of water contained in​ 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water is 0.03 gallon. You select a random sample of 50 ​bottles, and the mean amount of water per​ 1-gallon bottle is 0.992 gallon.   a. Is there evidence that the mean amount is different from 1.0 ​gallon? (Use α=0.01​.)   Let μ be the population mean. Determine the null​ hypothesis, H0​, and the alternative​ hypothesis, H1.   H0​: μ ____ H1​: μ ____   What is the test​ statistic?   ZSTAT= _________ ​(Round to two decimal places as​ needed.)   What​ is/are the critical​ value(s)? (Use α=0.01​.)   ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)   What is the final​ conclusion?   A. Fail to reject H0. There is not sufficient evidence that the mean amount is different from 1.0 gallon.   B. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.   C. Reject H0. There is not sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.   D. Reject H0. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...