To construct a confidence interval for the difference between two population means μ1−μ2​, use the formula shown below when both population standard deviations are​ known, and either both populations are normally distributed or both n 1 ≥30 and  n2 ≥30. ​Also, the samples must be randomly selected and independent.  The descriptive statistics for the annual salaries from a random sample of microbiologists from two regions are shown below. Construct a​ 95% confidence interval for the difference between the mean annual salaries   x1=​$105,020 1 n 1=44 and σ1equals=​$909 x 2 = 85,260​, n 2 = 35​, and sigma 2=​$9110   Complete the​ 95% confidence interval for 2μ1−μ2 below.

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 + ...