Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years. In the 1950's the average score on the Child Manifest Anxiety Scale was µ = 15.1. A sample of n = 16 of today’s children produces a mean score of M= 23.3 with SS = 240.(a)Based on the sample, has there been a significant change in the average level of anxiety since the 1950s? Use a two-tailed test with α = 0.01. State the null and research hypothesis  Sketch the sampling distribution and shade the part of distribution you're interested in Show calculations of the standard error and t score

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 + ...