1. The mean monthly salary of a random sample of 36 faculty members of Philippine Western University is P10,000 with a standard deviation of P1,000, while the mean monthly salary of a random sample of 35 faculty members of Central Luzon University is P10,500 with a standard deviation of P1,200. Is there a significant difference in the mean salaries received by the teachers of the two schools? Use an ? = 0.01 a. Use the traditional method and the b. P-Value method c. Construct a 99% confidence interval for the difference in ?1 − ?2.

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 + ...