Question

A group of Industrial Organizational psychologists wanted to test if giving a motivational speech at the end of a meeting would encourage office workers to have a higher output to their work based on the numbers of sales each worker made. The group tested 10 participants that were in two conditions where one meeting ended in a motivational speech and another were no motivational speech was given. Here are the number of sales that was produced by the 10 participants for both conditions:

Yes speech: 2, 6, 1, 9, 3, 12, 8, 0, 5, 1

No speech: 3, 0, 5, 10, 1, 8, 2, 1,9, 11

Use the four steps of hypothesis testing to find out if there is a significant difference between the two groups, using APA format to answer the question.

Answer 1

Explanation:

Corresponding number of sales that was produced by the 10 participants for both conditions form matched pairs.

The data for the test are the differences between the number of sales that was produced by the 10 participants for both conditions

μd = the​ number of sales produced by workers who were given motivational speech at the end of the meeting minus the​ number of sales produced by workers who were not given motivational speech at the end of a meeting

Yes speech No speech diff

2 3 - 1

6 0 6

1 5 - 4

9 10 - 1

3 1 2

12 8 4

8 2 6

0 1 - 1

5 9 - 4

1 11 - 10

Sample mean, xd

= (- 1 + 6 - 4 - 1 + 2 + 4 + 6 - 1 - 4 - 10)/10 = - 0.3

xd = - 0.3

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (- 1 + 0.3)^2 + (6 + 0.3)^2 + (- 4 + 0.3)^2 + (- 1 + 0.3)^2 + (2 + 0.3)^2 + (4 + 0.3)^2 + (6 + 0.3)^2 + (- 1 + 0.3)^2 + (- 4 + 0.3)^2 + (- 10 + 0.3)^2 = 226.1

Standard deviation = √(226.1/10

sd = 4.75

(M = - 0.3, SD = 4.75)

1) We would set up the hypothesis

For the null hypothesis

H0: μd = 0

For the alternative hypothesis

H1: μd ≠ 0

This is a two tailed test

The distribution is a students t.

2) The decision rule is to reject H0 if the level of significance is greater than the p value

Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (- 0.3 - 0)/(4.75/√10)

t = - 0.2

We would determine the probability value by using the t test calculator.

p = 0.845927

4) Assume alpha = 0.05

Since alpha, 0.05 < than the p value, 0.845927, then we would fail to reject H0. Therefore, there is a significant difference between the two groups