b) A machine fills cans with soft drinks so that their contents have a volume of 330ml. Over a period of time, it has been established that the volume of liquid in the cans follow a normal distribution with mean of 335 ml and standard deviation of 3 ml. A setting on the machine is altered, following which the operator suspects that the mean volume of liquid discharged by the machine into the cans has decreased. He takes a random sample of 50 cans and finds that the mean volume of liquid in these cans is 334.6 ml. Does this confirm his suspicion? Test at the 5% level of significance.

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 + ...