A large software company gives job applicants a test of programming ability, and the mean score for the test has been 150 in the past. Twenty-five applicants are randomly selected from one large university and they produce a mean score of 155, with a standard deviation of 12. At a significance level of 0.025, does this indicate that the sample comes from a population with a mean score greater than 150 Interpret the random variable X using the context of the problem Interpret the random variable using the context of the problem Use proper notations to write the Null and Alternative Hypothesis What is the sample size? What is the population standard deviation? What is the sample standard deviation? Calculate the test statistic Find the p-value? Why did you make the decision in 10)?

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 + ...