2. The standard error of the independent measures t provides an estimate of the standard distance between a sample mean diffrence (Mean-1 - Mean-2) and the population mean difference (mu-1 - mu-2). When the two samples come from the same population (when Ho is true), the standard error indicates the standard amount of error (distance) between the two sample means.
4. As the difference between the two sample means increases, the value of the t statistic increases. As the variability of the scores increases, the value of t decreases (becomes closer to zero).
6. The null hypothesis states that sex-type has no effect on depression, Ho: mu-1 - mu-2 = 0. For a one-tailed test, the critical value is t = 1.734. The pooled variance is 80, the standard error is 4, and t(18) = 2.00. Reject Ho and conclude that the traditional subjects are signifcantly more depresssed that the androgynous subjects.
8. a. There is a total of 26 subjects in the two samples combined.
b. With df = 24 and alpha = .05 the critical region consists of t values beyond plus/minus 2.064. The t statistic is in the critical region. Reject Ho and conclude that there is a significant difference.
c. With df = 24 and alpha = .01 the critical region consists of t values beyond plus/minus 2.797. The t statistic is not in the critical region. Fail to reject Ho and conclude there is no significant difference.
10. Ho: (mu-1 - mu-2) less than/equal to 0 (no increase). H1: (mu-1 - mu-2) greater than 0 (incrase). Pooled variance = 30 and t(13) = 3.67 which is beyond the one-tailed critical boundary of t = 1.771. Reject Ho and conclude that fatigue has a significant effect.
12. The null hypothesis states that personality has no effect on frustration, Ho: mu-1 - mu-2 = 0. With alpha = .01 the critical region consists of t values beyond plus/minus 2.977. The pooled variance is 100, the standard error is 5, and t(14) = 2.60. Fail to reject Ho and conclude that there is no significant difference between the two personality groups.
14. The null hypothesis states that the imagined factors have no effect on persistence, Ho: mu-1 - mu-2 = 0. With alpha = .05 the critical region consists of t values beyond plus/minus 2.074. The pooled variance is 24, the standard error is 2, and t(22) = 3.00. Reject Ho and conclude that there is a significant difference between the two conditions.
16. The null hypothesis states that pollution has no effect on life expectancy, Ho: mu-1 - mu-2 = 0. The critical region consists of t values beyond plus/minus 2.048. Pooled variance = 540 and t(28) = -3.67. Reject Ho and conclude that pollution has a significant effect on life.
18. The null hypothesis states that environment has no effect on development, Ho: mu-1 - mu-2 = 0. With alpha = .01 the critical region consists of t values beyond plus/minus 2.878. For the rich rats, mean = 26 and SS = 214. For the poor rats, mean = 34.2 and SS = 313.61. The pooled variance is 29.31, the standard error is 2.42, and t(18) = 3.39. Reject Ho. The data indicate a significant difference between the two environments.
20. The null hypothesis states that there is no difference in
difficulty
between the two problems, Ho: mu-1 - mu-2 = 0. With alpha = .01 the
critical
region consists of t values beyond plus/minus 3.355. With the tacks in
the box, mean = 107.2 and SS = 6370.8. With the tacks and box separate,
mean = 43.2 and SS = 1066.80, and t(8) = 3.32. Fail to reject Ho. The
data are not sufficient to indicate a significant difference between the
two conditions.