A tire producer wants to test whether the mean diameter of the tires produced on a given day equals 36 inches.  Whether the mean diameter is less than 36 is of little or no importance, but it is important for the firm to determine whether or not the mean diameter is more than 36 inches.  The firm chooses a random sample of 49 tires, and find that their mean diameter is 36.4 inches and the sample standard deviation is 0.8 inches.  Should the firm accept the hypothesis that the mean diameter is 36 inches?  Use alpha = 0.05. What is the null hypothesis? What is the alternative hypothesis? What distribution are you using? What test are you running? What is your conclusion?

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 + ...