A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical value approach. (A) Calculate the test statistic (clearly label it as either z or t as needed); (2) Embed a photo of a manual sketch of the distribution with the critical region(s) shaded and the test-statistic clearly labeled; (3) Determine whether to reject or fail to reject H0, (4) Write a conclusion based on the rejection or failure to reject H0.  All math must be typeset appropriately using the Rich Text Editor. You must embed the sketch of the critical region within the Rich Text Editor adhering to the Photo Upload Guidelines. = 25, n = 40, σ = 1.5, H0: μ = 22 Ha: μ ≠ 22 **claim** α = 0.05

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 + ...