Question

18. 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 workers 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

Answer:

The 4 steps of hypothesis testing are:

Step 1 : State null hypothesis and alternative hypothesis.

Step 2 : Compute the test statistics value.

Step 3 :Identify the critical value or the P-value by the tables.

Step 4 : Make a conclusion of the hypothesis.

Step1:

H0 : There is a no significant difference between the two groups.

H1 : There is a significant difference between the two groups.

Symbolically: H0: vs H1:

Step2:

the formula for test statistics is

n1, n2 are sample sizes of two samples, and   are sample means and , are sample variances. The means and sample variances can be calculated by using formulas of mean and variance from given data.

Here we use excel output of summary statistics:

Yes speech		No speech
Mean	4.7	Mean	5
Standard Error	1.26535	Standard Error	1.316561
Median	4	Median	4
Mode	1	Mode	1
Standard Deviation	4.001389	Standard Deviation	4.163332
Sample Variance	16.01111	Sample Variance	17.33333
Kurtosis	-0.74015	Kurtosis	-1.80257
Skewness	0.600416	Skewness	0.277145
Range	12	Range	11
Minimum	0	Minimum	0
Maximum	12	Maximum	11
Sum	47	Sum	50
Count	10	Count	10

From this output: n1=10 and n2=10,   = 4.7 and  =5 , = 16.0111 and  = 17.33333

Hence test statistics is

Step3:

Now the critical value for this test is T(crit) = 2.101 ( from table with alpha=0.05 and df= n1+n2-2 = 10+10-2 = 18)

Step4:

Conclusion:

If value of test statistics is greater than critical value then we reject H0. But here value of test statistics is less than critical value (i.e -0.164289 < 2.101 ) hence we Accept H0.

As we accept H0, we conclude that there is a no significant difference between the two groups.

The excel output for two sample t- test (for reference):

t-Test: Two-Sample Assuming Unequal Variances
	Yes speech	No speech
Mean	4.7	5
Variance	16.01111	17.33333
Observations	10	10
Hypothesized Mean Difference	0
df	18
t Stat	-0.16429
P(T<=t) one-tail	0.435667
t Critical one-tail	1.734064
P(T<=t) two-tail	0.871334
t Critical two-tail	2.100922

As our hypothesis is two tailed we used t Critical two tailed. And we accept the H0.