The teachers in a large local high school want to see if the mean number of students per class for their high school is larger than the mean class size reported by the state. According to state records, the mean class size for all high schools in the state is 29.7 students per class. The teachers want to conduct a significance test at the α = 0.10 significance level of H0: μ = 29.7 versus Ha: μ > 29.7, where µ is the true mean number of students in each class in the high school. The teachers select a random sample of 20 different classes from all of the classes at the high school and calculate the sample mean to be 31.2 students per class with a standard deviation of 2.72 students per class. Using Table B, which of the following is the range the P-value is between? Assume that the conditions are met.
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 + ...
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