(b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 100 applications provided a sample mean x = 833? A confidence interval for a population mean, u, is found by adding and subtracting the margin of error, E, to the given sample mean, as follows. Recall that z, is the standard normal random variable corresponding to a particular level of confidence and n is the sample size. x+ E, where E = z2 A sample of 100 applications provided a mean of 833 and the standard deviation is known to be 150. Thus, n = and . Now the value of za is needed. A 95% confidence interval is to be found. The margin of error corresponding to a 95% confidence level is needed, which is calculated using z2. Common values for z, for various confidence levels are given below. * Za/2 Confidence Level a 90% 0.10 0.05 1.645 95% 0.05 0.025 1.960 99% 0.01 0.005 2.576 For a 95% confidence level, the necessary value for z/2 is

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 + ...