Question

Friedman and Rosenman (1974) classified people into two categories: Type A personalities and Type B personalities. Type A's are hard-driving, competitive, and ambitious. Type B's are more relaxed, easy going people. One factor that differentiates these two groups is the chronically high level of frustration experienced by Type A's, especially when doing statistical analyses. (Oftentimes Type A's have been known to suffer from numerical alexithymia.) To verify this aspect separate samples of Type A's and Type B's are obtained. The following frustration scores were obtained (note: the higher the score the greater the degree of frustration):

Type A                                    Type B

25                                            21

   23                                            16

   19                                            19

                                                   18

Part A.   What are the degrees of freedom and the critical value (α = .05) for this problem?

df =_______________ SHOW WORK FOR THIS

t_crit = ______________ SHOW WORK FOR THIS

Part B. Calculate the pooled variance estimate ________. SHOW WORK FOR THIS

Part C. Compute the observed t-statistic ____________. SHOW WORK FOR THIS

Answer 1

Solution: Part A. What are the degrees of freedom and the critical value (α = .05) for this problem?

Where:

is a number of students in Type A

is a number of students in Type B

can be found using the t distribution table at significance level for df = 5. Here we have a right-tailed alternative hypothesis, therefore we will have only one critical value. Using the t distribution table, we have:

Part B. Calculate the pooled variance estimate

Answer: The formula for pooled variance estimate is:

Where:

is the sample variance of Type A

is the sample variance of Type B

Therefore, the pooled variance is 6.3333

Part C. Compute the observed t-statistic​

Answer: The observed t-statistic is:

Where:

is the sample mean of Type A

is the sample mean of Type B

  

  

Therefore, the observed t-statistic is 1.99