Question

Scenario:

Assuming the data below is from a randomly sampled population of Psychology Major’s and the scores represent Self-Esteem. All majors have a mean of µ=15 and standard deviation of σ=5.

Data:

10, 12, 18, 12, 15, 14, 11, 10, 14, 17, 15, 13, 12

Instructions:

1. For the data above, calculate the mean, median, mode, range, sum of squares, variance, and standard deviation and put them into an APA style table (If you use JASP, then you can copy the APA table from the results).  

10 points

2. Write out the hypotheses for testing self-esteem of Psychology Majors and the All Majors are the same or different. This should be a one tailed test (are Psychology majors higher or lower – you decide), using an alpha α =.05.

10 points

3. Calculate the z value for a hypothesis test. Report in APA your findings (including the critical z value used to determine if there is a significant difference).

10 points

4. Is the z-score you calculated statistically significant? Explain your answer.

10 points

5. What do you conclude? Write a short summary of your conclusions using the data from your analysis to support your conclusions.

10 points

Answer 1

Number	Values
1	10
2	10
3	11
4	12
5	12
6	12
7	13
8	14
9	14
10	15
11	15
12	17
13	18
Total	173
Count	13

Mean   

Median :- Is the Middle most value in the data set

7^th value in the data set is the middle most value

Median = 13

Mode :- Is the highest frequency in the data set

Values	Frequency
10	2
11	1
12	3
13	1
14	2
15	2
17	1
18	1

THe value 12 has been repeted 3 times in the data set

Mode = 12

Sum of squares   

Number	Values
1	10	10.94
2	10	10.94
3	11	5.33
4	12	1.71
5	12	1.71
6	12	1.71
7	13	0.09
8	14	0.48
9	14	0.48
10	15	2.86
11	15	2.86
12	17	13.63
13	18	22.02
Total	173	74.769

Subtracting the mean from rach value in the data set and taking the square of it.

= 74.769

Variance of the sample

Standard Deviation of sample  

Part 2)

Let   :- Mean of self-esteem of Psychology Majors.

To Test :-

H₀ :-   

Self-esteem of Psychology Majors is less than equal to the All Majors.

H₁ :-    

Self-esteem of Psychology Majors is geater than the All Majors.

Test Statistic :-

Test Criteria :-

Reject null hypothesis if   ( Since alternative hypothesis has > sign )

( Critical value calculate from Standard Normal Table )

= -1.22 < 1.64, hence we fail to reject null hypothesis

Conclusion :- We Accept Null Hypothesis

Self-esteem of Psychology Majors is less than equal to the All Majors.