ber under the ighting con. different conditions The expe tive illusions was 6.72 under the bright co MyStatLab conditions, a difference that was not significant, r(19)-1.62." Exp result to a person who has never had a course in statistics. Be sur researchers re The 'college at the beginning and end of their first year of the results in the following table 12 A study was done of personality characteristics of 100 students who were sketches of the distributions in your answer Difference Spring SD M Fall 3.84 SD 1.50* 15.32 Personality Scale Anxiety Depression 4.21 8.91 3.08 1 86.24 16.82 8.39 7.11 -23 60.12 89 32 6.87 6.02 22 89* 37.22 59 89 5.39 4.2 Introversion 38.11 Neuroticism DA 05,p<.01 (a) Focusing on the difference scores, figure the t values for each personal scale. (Assume that SD in the table is for what we have called S, the unbiase (b) Explain to a person who has never had a course in statistics what this tabl estimate of the population standard deviation.) means Set II 13. In each of the following studies, a single sample's mean is being compared to a population with a known mean but an unknown variance. For each study, de- tatLab cide whether the result is significant. Estimated Population Standard Sample Size (N) Population Mean (u) Sample Mean (M) Deviation Significance Level (a) (S) Tails (a) 16 100.31 2.00 100.98 1 (high predicted) (b) 16 05 .47 4.00 .00 2 16 68.90 .05 9.00 34.00 1 (low predicted) .01 14. Evolutionary theories often emphasize that humans have adapted to their physi cal environment. One such theory hypothesizes that people should spontane- ously follow a 24-hour cycle of sleeping and waking-even if they are not 99

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 + ...