Question

1. A researcher who works for a national retail chain is interested in changes in employee satisfaction during the holiday season. The table below contains employee satisfaction scores taken at two time points (August 1^st and December 1^st) from a sample of 12 employees. Higher scores indicate more satisfaction. Conduct a hypothesis test to determine if there is an increase or decrease in employee satisfaction from Time 1 to Time 2. Use alpha .05.

Employee Number	Time 1 Satisfaction	Time 2 Satisfaction
10012	8.5	6.5
10057	6.8	4
10089	6.5	4
10126	4.2	5.7
10023	7	6
10045	6	3
10094	7	6.5
10087	3	3
10145	4.5	3.5
10023	9	8.5
10062	8.5	4
10078	4	2.5

1. State the null alternative hypothesis.
2. Conduct the hypothesis test.
3. State your findings.
4. Report an effect size measure. Please use the formula that we used in class

Answer 1

Consider

a) X: Employee satisfaction at Time 1.

Y : Employee satisfaction at Time 2.

d= Difference in employee satisfaction from time 1 to time 2

: Mean difference in employee satisfaction from time 1 to time 2

We have to test the hypothesis that

There is an increase or decrease n employee satisfaction from time 1 to time time 2

i.e. Null Hypothesis-

against

Alternative Hypothesis- ( Two-tailed test)

b) Since samples are dependent we use paired t-test for testing of hypothesis.

The value of test statistic is

Employee Number	Time 1 satisfaction (x)	Time 2 satisfaction(y)	d=x-y	(d-dbar)^2
10012	8.5	6.5	2	0.2670
10057	6.8	4	2.8	1.7337
10089	6.5	4	2.5	1.0337
10126	4.2	5.7	-1.5	8.9001
10023	7	6	1	0.2336
10045	6	3	3	2.3004
10094	7	6.5	0.5	0.9669
10087	3	3	0	2.2002
10145	4.5	3.5	1	0.2336
10023	9	8.5	0.5	0.9669
10062	8.5	4	4.5	9.1005
10078	4	2.5	1.5	0.0003
Total			17.8	27.9367

Value of test statistic is

Degrees of freedom : n-1 =12 -1 =11.

Since test two tailed and value of test statistic t is 3.2243, p-value is obtained by

From t-table

P(t11> 3.2243) = 0.0040

p-value = 0.0080

c) Value of test statistic t = 3.2243

p-value = 0.0080

Alpha: level of significance = 0.05

Decision : Since p-value < alpha, we reject the null hypothesis.

Conclusion : There is sufficient evidence to conclude there is significant difference in employee satisfaction from time 1 to time 2.

d) By Cohen-d formula effect size is calculated by

Effect size = dbar / Sd

= 1.4833 / 1.5936

=0.9308 > 0.8

There is large effect.

i.e. There is highly significant difference between employee satisfaction from time 1 to time 2.