Question

 

SSHA score

Survey Study Habits and Attitude (SSHA) is a psychological test designed to measure motivation, habits and attitudes towards learning among college students in the United States. The scores on the SSHA range from 0 to 200. In a study at an American college, the results were included in the data file SSHA.SAV.

1- Give a descriptive description of the SSHA score, with mean, median, standard deviation and any other descriptive targets that can describe this data.

2- Are the SSHA slots normalized?

The study also indicates whether you are female (sex = 0) or male (sex = 1).

3- Provide a 95% confidence interval for the average for women and men individually.

4- Show that confidentiality ranges for women and men are overlapping.

A researcher of you claims that the impossible can be statistically significant difference between the SSHA scores as long as the confidence intervals are (partially) overlapping. What do you mean about this claim?

5- Test the hypothesis that the SSHA scores are equal for men and women. What is the conclusion? Be sure to check the assumptions that lie behind the test

6- Summarize the conclusion in point 5 to what you got in point 4, and what can you tell your alleged researcher?

SPSS FILE 1.

Score

154
109
137
115
152
140
154
168
101
103
126
126
137
165
165
128
180
148
108
140
114
91
175
115
126
92
169
146
109
132
75
88
113
151
70
115
169
104

SPSS FILE 2.

SEX

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Answer 1

 

Based on the information provided:

The descriptive statistic measures can be determined using the below formulas:

Mean of a sample:

Sample variance and Sample Standard deviation:

SEX	SEX	Score		SEX	SEX	Score
0	Female	154		1	Male	108
0	Female	109		1	Male	140
0	Female	137		1	Male	114
0	Female	115		1	Male	91
0	Female	152		1	Male	175
0	Female	140		1	Male	115
0	Female	154		1	Male	126
0	Female	168		1	Male	92
0	Female	101		1	Male	169
0	Female	103		1	Male	146
0	Female	126		1	Male	109
0	Female	126		1	Male	132
0	Female	137		1	Male	75
0	Female	165		1	Male	88
0	Female	165		1	Male	113
0	Female	128		1	Male	151
0	Female	180		1	Male	70
0	Female	148		1	Male	115
	Average or Mean	139.33		1	Male	169
	Standard Deviation	23.33		1	Male	104
	Variance	544.47			Average or Mean	120.10
	Range	101-180			Standard Deviation	30.67
	Maximum	180			Variance	940.73
	Minimum	101			Range	70-175
	Mode	154			Maximum	175
	Median	138.5			Minimum	70
					Mode	115
					Median	114.5

1- Give a descriptive description of the SSHA score, with mean, median, standard deviation and any other descriptive targets that can describe this data.

Based on the analysis:

• Average SSHA Score for Female = 139.33
• Standard deviation for SSHA score for Female = 23.33
• Sample size for Female = 18
• Median SSHA score for Female = 138.5

• Average SSHA Score for Male = 120.10
• Standard deviation for SSHA score for Male = 30.67
• Sample size for Male = 20
• Median SSHA score for Male = 114.5

2- Are the SSHA slots normalized?

The study also indicates whether you are female (sex = 0) or male (sex = 1).

3- Provide a 95% confidence interval for the average for women and men individually.

• Since population standard deviation is not known, therefore t-statistic will be used for confidence interval
• 95% confidence interval can be determined using the formula:
• For Female
  • 
  • 
• For Male
• 
• 

4- Show that confidentiality ranges for women and men are overlapping.

• Yes confidentiality ranges for women and men are partially overlapping based on the above calculated values.

A researcher of you claims that the impossible can be statistically significant difference between the SSHA scores as long as the confidence intervals are (partially) overlapping. What do you mean about this claim?

• If there are non-overlapping confidence intervals, then the two statistic parameters are necessarily significantly different but if they have overlapping confidence intervals, it is not necessarily true that they are not significantly different.

5- Test the hypothesis that the SSHA scores are equal for men and women. What is the conclusion? Be sure to check the assumptions that lie behind the test.

• In this case, t-Test for difference in Population Means can be performed
• Null Hypothesis
• Alternative Hypothesis
• Assuming population variances are equal, pooled variance can be calculated using the formula:
• 
• The test-statistic T can be calculated using the formula:
• 
• Degree of freedom = n1 + n2 - 2 = 36
• P-value corresponding to t-value 2.1565 with 36 degree of freedom is 0.0378. Since this value is less than the significance level 0.05, therefore Null Hypothesis is rejected.
• Based on the evidence, there is statistically significant difference between the SSHA scores between female and male at a significance level of 0.05.

6- Summarize the conclusion in point 5 to what you got in point 4, and what can you tell your alleged researcher?

• In this case, there are overlapping confidence intervals for the mean of two different populations (female and male). However, the t-test for the difference in population mean is significant implying that the two population means are statistically different.