Suppose researchers wish to determine if the mean birth weight of infants in 1961 is significantly lower than the historical average, 121121 ounces. Suppose the population standard deviation of birth weights is equal to 1919 ounces. Use software to calculate the sample mean (?⎯⎯⎯x¯) for these data. Then, conduct a one‑sample ?z‑test to test the researchers' hypothesis at the ?=0.05α=0.05 level. What are the standard error (SE), the ?z‑statistic, and the ?z‑critical value for this test? Please round all answers to the nearest three decimal places. Sample mean 119.81.

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 + ...