10.18. A plant manager randomly divides her employees into two groups. One group

Question

10.18. A plant manager randomly divides her employees into two groups. One group (Group A) includes 32 employees and the second one (Group B) includes 30 employees. After dividing the employees, the manager wants to confirm that the two groups are indeed similar in performance. He hypothesizes that there is no statistically significant difference between the two groups. To compare the two groups, the plant manager use ratings given by the employees' front-line supervisors at the end of the previous year. The rating scale ranges from 5 (excellent employee) to 1 (on the brink of termination). Using these ratings, the manager conducts a t test to determine whether the two groups are similar. The results are as follows: Group n Mean SD t A 32 3.66 1.31 2.008 B 30 3.00 1.26 t crit(.05,df)=2.0; t crit(.02,df)=2.390; t crit(.01 ,df)=2.660

a. Which t test was used and why?

b. What were the degrees of freedom?

c. What are the manager's conclusions?

10.19. Joe, a new manager suspects that the 23 new employees assigned to his department have lower levels of social skills than the new employees hired into the all the other departments in the rest of the company. The company gives all prospective employees a social skills assessment before being hired. The mean score obtained by Joe's new employees is 635.13 and the mean score of all 678 new employees recently hired by the company on the same social skills assessment is 430 (fl=430). A t test is used to compare the social skills assessment scores of Joe's new employees to all the new employees in the company. The results of the t test are: Mean score= 635.13 SD= 71.53 t value= 3.75 p=.0001 d. a.

Which t test is used and why? Independent

What are the degrees of freedom (df)? 22

c. What are Joe's conclusions?

11.16. An ANOVA procedure is used to analyze data from a study comparing scores of three groups. Following are the obtained mean squares and the appropriate critical values for the F ratio at p=.05 and p=.01 Fcrit(.05,2,20) = 3.49 and Fcrit(.O1,2,20) = 5.85

a. Compute the obtained F ratio.

b. Determine whether the results are statistically significant.

c. Report your conclusions.

Explanation / Answer

Answer 10.18

Part a

Here, the two sample t test with equal population variances is used because both groups are selected from the same population.

Part b

The degrees of freedom is given as d.f. = 32 + 30 – 2 = 60

Part c

Reject the null hypothesis that two groups are equal at 0.05 level of significance

Do not reject the null hypothesis that two groups are equal at 0.02 level of significance

Do not reject the null hypothesis that two groups are equal at 0.01 level of significance

Answer 10.19

Part a

Here, the two sample t test with unequal population variances is used because the population variances for two groups are not same and both groups is chosen from different populations.

Part b

The degrees of freedom = d.f. = 22

Part c

Reject the null hypothesis that there is no any significant difference in the levels of skills between the new employees and all employees as there is a very small p-value (0.0001) is given as compared to the significance level 0.01 or 0.05.

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