The literature suggests that trust is related to agreement. A social psychologis

ID: 3357966 • Letter: T

Question

The literature suggests that trust is related to agreement. A social psychologist wants to know if this holds for the employees. The psychologist obtains a random sample of employees from a company and has them fill out a survey that categorizes them into the following categories: low moderate, and high trust of supervisors. The employees are then asked to rate their level of agreement concerning job decisions made by their supervisors. The data are below with higher scores indicating more agreement. What can the psychologist conclude with an alpha of .01? The literature suggests that trust is related to agreement. A social psychologist wants to know if this holds for the employees. The psychologist obtains a random sample of employees from a company and has them fill out a survey that categorizes them into the following categories: low moderate, and high trust of supervisors. The employees are then asked to rate their level of agreement concerning job decisions made by their supervisors. The data are below with higher scores indicating more agreement. What can the psychologist conclude with an alpha of .01? The literature suggests that trust is related to agreement. A social psychologist wants to know if this holds for the e the following categories: low, moderate, and high trust of supervisors. The employees are then asked to rate their l can the psychologist conclude with an of 0.01? low moderate high 23 28 18 30 28 21 20 24 23 24 26 24 21 18 15 17 29 26 20 16 25 27 17 15 19 18 14 16 20 21 17 16 21 a) What is the appropriate test statistic? Select b) Compute the appropriate test statistic(s) to make a decision about Ho !; Decision :!--Select p-value = c) Compute the corresponding effect size(s) and indicate magnitude(s). lect d)Make an interpretation based on the results. O At least one of the trust categories differ in agreement with the supervisor. O None of the trust categories differs in agreement with the supervisor.

Explanation / Answer

Part a

The appropriate test statistic is F test statistic (ANOVA F test).

Part b

Here, we have to find the p-value for ANOVA F test. The required ANOVA table based on the given data is summarized as below:

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Low

216

7.090909

Moderate

269

22.41667

31.35606

High

289

24.08333

12.26515

ANOVA

Source of Variation

P-value

F crit

Between Groups

237.1667

118.5833

7.015088

0.002892

3.284918

Within Groups

557.8333

16.90404

Total

795

P-value = 0.002892

= 0.01

P-value < = 0.01

So, we reject the null hypothesis.

Decision: Reject the null hypothesis H0.

Part c

Effect size = 2 = SS Between /SS Total

Effect size = 2 = 237.1667 / 795 = 0.298323

We know that if

2 = 0.8 or more, effect size is large

2 = 0.5 to 0.8, effect size is moderate

2 = 0.2 to 0.5, effect size is small

We have 2 = 0.298323, so magnitude is small.

Part d

Interpretation:

At least one of the trust categories differ in agreement with the supervisor.

(We reject the null hypothesis that none of the trust categories differs in agreement with the supervisor, this means there is sufficient evidence to conclude that at least one of the trust categories differ in agreement with the supervisor.)