The Central Limit Theorem is important for a number of reasons. First, because the Central Limit Theorem makes a claim about the normal distribution of a large number of values, it suggests the appropriateness of using parametric forms of statistical analysis (such as the independent samples t test) instead of non-parametric versions of these tests (such as the Mann-Whitney-U test). Second, the Central Limit Theorem justifies the practice of reaching conclusions about a population from a sample of sufficient size.
I would expect these means to be very similar, because of the Central Limit Theorem. Assume a distribution of scores with n = 100,000 that is broken into 100 samples of 1,000. If the assumptions of the Central Limit Theorem of met, we can assume that the means of these 100 samples are very close to the mean of all scores in the population of 100,000.
The value of each score would have to be 400. There is no score lower than 400 in the distribution; therefore, to get a mean of 400, we can only build a sample that has 400 for each of its 10 values.
The value of each score would have to be 600. There is no score higher than 400 in the distribution; therefore, to get a mean of 600, we can only build a sample that has 600 for each of its 10 values.
The most common mean score would be 500, as that is the mean of the population.
There would be no distribution per se; there would just be whatever value was drawn in the 1-item sample’in the histogram, this would be a vertical line, not a column or columns.
SPSS Assignment #1
First, the hypotheses should be set up:
H10: Mean hours for CGK ? mean hours for Pre-Voc.
H1A: Mean hours for CGK > mean hours for Pre-Voc.
H20: Mean hours for females ? mean hours for men.
H1A: Mean hours for females > mean hours for men.
Set Alpha to 0.05; thus, reject the null hypothesis if p < 0.05. Note that the hypotheses are one-tailed, so the obtained p value in SPSS has to be divided by 2; SPSS does not automatically present 1-tailed p values in t tests. An independent samples t test indicated that there a significant effect of program on hours, t(15) = -2.474, such that, at an Alpha of 0.05, the hours associated with PVC (M = 485.22, SD = 36.389) were lower than the hours associated with CGK (M = 543, SD = 58.615). The p value of the two-tailed test was 0.026; therefore, the p value of the one-tailed test is 0.013. The null hypothesis should be rejected. The mean hours for CGK were indeed higher than the mean hours for Pre-Voc. Next, An independent samples t test indicated that there a significant effect of gender on hours, t(15) = -3.076, such that, at an Alpha of 0.05, the hours associated with men (M = 481, SD = 27.354) were lower than the hours associated with women (M = 547.75, SD = 58.463). The p value of the two-tailed test was 0.008; therefore, the p value of the one-tailed test is 0.004. The null hypothesis should be rejected. The mean hours for women were indeed higher than the mean hours for men. Bank Tellers Part 1 The coefficients are all negative because there is an inverse relationship between performance and these 2 forms of errors. In other words, as the errors go down, the performance goes up, and, as the errors go up, the performance goes down. If we graphed this relationship as an OLS line of best fit, it would have a negative slope. Part 2 We don't know anything about the actual number of overages and shortages. We can only reach conclusions about the relationship between these 2 measures and performance. We cannot determine, from these data, which group had more overages or shortages. Part 3 The fact that the magnitude of the negative correlations is greater for the Black tellers indicates that their performance is more heavily affected by shortages and overages; it is possible that, because of racial bias, shortages and overages committed by Black tellers are more readily used to inform performance evaluations. SPSS Exercise 2 H10: There is no significant correlation between premorbid and hours. H1A: There is a significant correlation between premorbid and hours. Alpha = 0.05. The correlation between hours and premorbid is strong, positive, and significant, R = 0.639, p = 0.006. When premorbid hours is regressed on hours in the program, it can be seen that there is a significant effect of premorbid on hours, F(1, 15) = 10.365, p = 0.006. The R2 of this OLS regression is 0.409, indicating that nearly 41% of the variation in hours can be explained by variation in premorbid hours. The OLS equation is as follows: Hours = (Preborbid Hours)(1.857) + 448.496 Hence, for every 1-unit increase in premorbid hours, participants had 1.857 more hours in the program.