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CHAPTER 9

1/ A z- score is used when the population standard deviation or variance is known. The t statistic is used when the population variance or standard deviation is unknown. You use the sample data to estimate the variance and the standard error.

2/
a/ Increase the variability of the scores: decrease the value of t
b/ Increase the number of scores in the sample: Increase the value of t
c/ Increase the difference between the sample mean and the population mean: increase the value of t

3/ the sample variance s² in the t formula is an estimated value and contributes to the variability.

4/ When df values are small; the t distribution tend to be flatter and more spread out

5/
a/ n= 16 M = 45 SS = 960
s² = 960 /( 16-1) = 64 s = 8
estimate standard error : s (M) = 8/ 4 = 2

b/ The sample standard deviation describes the average distance between X and M for the scores in the sample. The standard error describes the average distance between a sample mean, M, and the population mean, m, for a sample with these characteristics
( n =16 and s = 8)

6/
a/ M = 8 /4 = 2 s² = 12 /3 s = 2

b/ Estimated standard error for M : = ( 4 / 4)² = 1

9/ m = 50 M = 56 s = 8

a/ n = 4 s = (64/4 )½ = 4 t = ( 56- 50) / 4 = 1.5
This is not greater than the critical value of 3.168, so there is no significant effect.

b/ n = 16 estimate standard error is = (64/ 16 )½ = 2 t = ( 56- 50) / 2 = 3

This value is greater than the critical value of 2.131 , so we reject the null hypothesis and conclude that there is a significant treatment effect.

17/ n = 25 M = 87...