Reference no: EM13953518

Introduction to Statistics

Part A- Outputs:

1. A sample of university employees had been assembled. An output concerning their education is presented below. Study the output and answer the following questions:

a. What is the mean, median and the standard deviation?

b. Firstly, what is the interquartile range, and secondly, how many education years has the most educated employee?

c. What is the number of education years that 36% of the sample has that number of education years or below it? Answer the same question for 83%.

d. Firstly, how many employees has 12 education years or less? Secondly, how many employees have missing values in the variable education years?

Statistics

Highest Year of School Completed

N	Valid	1510
	Missing	7
Mean		12.88
Median		12.00
Mode		12
Std.  Dev iation		2.984
Variance		8.904
Range		20
Minimum		0
Maximum		20
Sum		19455
Percentiles	10	9.00
	25	12.00
	36	12.00
	50	12.00
	75	15.00
	83	16.00

Highest Year of School Completed

		Frequency	Percent	Valid Percent	Cumulativ e Percent
Valid	0	2	.1	.1	.1
	3	5	.3	.3	.5
	4	5	.3	.3	.8
	5	6	.4	.4	1.2
	6	12	.8	.8	2.0
	7	25	1.6	1.7	3.6
	8	68	4.5	4.5	8.1
	9	56	3.7	3.7	11.9
	10	73	4.8	4.8	16.7
	11	85	5.6	5.6	22.3
	12	461	30.4	30.5	52.8
	13	130	8.6	8.6	61.5
	14	175	11.5	11.6	73.0
	15	73	4.8	4.8	77.9
	16	194	12.8	12.8	90.7
	17	43	2.8	2.8	93.6
	18	45	3.0	3.0	96.6
	19	22	1.5	1.5	98.0
	20	30	2.0	2.0	100.0
	Total	1510	99.5	100.0
Missing	NA	7	.5
Total		1517	100.0

2. Researcher which studies the field of eating disorders checked the correlation between subject's body image ranking and the degree to which they restrict food intake. Study the output and answer the following questions:

	Body perception	Restriction of f ood intake (f asting)
Body   perception Pearson Correlation	1	.383**
Sig. (2-tailed)		.000
N	217	217
Restriction  of  f ood Pearson Correlation	.383**	1
intake  (f asting)   Sig. (2-tailed)	.000
N	217	217

1. What can be inferred from the table?

a. There is a significant negative correlation between the variables.

b. There is a moderately negative correlation between the variables.

c. There is a moderately positive correlation between the variables.

d. There is a weak positive correlation between the variables.

2. Report the correlation.

3. The following output present a regression done in order to predict the number of SMS messages a person sends to his\hers partner by the length of the relationship (in years). Study the output and answer the following questions:

Regression

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	-.661(a)	.436	.435	123.540

a. Predictors: (Constant), Duration of relationship (years)

ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	6010.000	1	100.000	365.381	.000(a)
	Residual	7776.340	472	160.840
	Total	13776.340	473

a. Predictors: (Constant), Duration of relationship (years) b  Dependent Variable: SMS

Coefficients(a)

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta	B	Std. Error
1	(Constant)	15.178	2821.912	.661	-6.496	.000
	Duration of relationship (years)	-0.183	204.547		19.115	.000

a. Dependent Variable: SMS

1. What is the percentage of explained variance?

2. Write the regression line equation.

3. Brad and Angelina are married for 25 years. According to this analysis, how many SMS messages should Brad send Angelina?

4.  A researcher is conducting a research on the effects of sociability on mood. He is using a questionnaire in order to assess sociability. Study the output concerning the reliability check and answer the following questions:

Reliability

Scale: sociability

Case Processing Summary

		N	%
	Valid	198	99.0
Cases	Excludeda	2	1.0
	Total	200	100.0

a. Listwise deletion based on all variables in the procedure.

Reliability Statistics

Cronbach's Alpha	Cronbach's Alpha Based on Standardized Items	N of Items
.627	.659	8

Inter-Item Correlation Matrix

	1	2	3	4	5	6	7	8
1. I like to see friends	1.000	.605	-.024	.189	.501	-.435	.451	.396
2. I talk a lot with friends on the phone	.605	1.000	-.001	.362	.492	-.837	.509	.424
3. I like chocolate	-.024	-.001	1.000	.003	.009	.001	-.001	-.017
4. I go to a lot of parties	.189	.362	.003	1.000	.408	-.557	.430	.411
5. I have many friends	.501	.492	.009	.408	1.000	-.243	.675	.510
6. I like to read alone at home	-.435	-.837	.001	-.557	-.243	1.000	-.408	-.650
7. Romantic relationship are important	.451	.509	-.001	.430	.675	-.408	1.000	.495
8. I feel good with my social status	.396	.424	-.017	.411	.510	-.650	.495	1.000

Item-Total Statistics

	Scale Mean if Item Deleted	Scale Variance if Item Deleted	Corrected Item- Total Correlation	Squared Multiple Correlation	Cronbach's Alpha if Item Deleted
1. I like to see friends	17.4495	26.188	.515	.443	.561
2. I talk a lot with friends on the phone	17.2374	24.009	.555	.472	.534
3. I like chocolate	16.1919	29.811	.007	.018	.686
4. I go to a lot of parties	15.9697	23.826	.399	.330	.571
5. I have many friends	16.7273	21.753	.666	.546	.489
6. I like to read alone at home	14.6768	35.540	-.320	.196	.753
7. Romantic relationship are important	17.0556	23.220	.634	.528	.512
8. I feel good with my social status	16.4192	23.260	.473	.397	.547

1. What is the number of subjects whose answers had been entered to the reliability check?

2. What is the internal reliability of the sociability questionnaire?

3. Which item (or items) would you suggest to change or omit (leave out)? Explain why, both from a statistical point of view and from the theoretical point of view.

Part B - statistical comprehension:

1. Study the table and answer the following questions:

Taken from Somer, E., Maguen, S., Or-Chen, K. & Litz, B. (2008). Managing Terror: Differences between Jews and Arabs in Israel. International Journal of Psychology, 42, 1-9.

Table 1

Demographic Variables of Jewish-Israelis and Arab-Israelis

Demographic Characteristics	Jewish- Israelis (n = 100)	Arab- Israelis (n = 100)	Statistic comparing the two groups
	M = 43.60   (SD = 16.76)	M = 36.62 (SD=13.02)	t(198) = 10.82**
Age (years)
Gender Male Female	24% 76%	34% 66%	χ2  = 2.43
Marital status Married Non-Married	60% 40%	73% 27%	χ2  = 3.79
Religion Jewish Christian Muslim Druze	100% 0% 0% 0%	0% 72% 27% 1%	χ2  = 200**

Table 1

Demographic Variables of Jewish-Israelis and Arab-Israelis

Demographic Characteristics	Jewish- Israelis (n = 100)	Arab- Israelis (n = 100)	Statistic comparing the two groups
Religiosity Religious Traditional Seculra	10% 26% 64%	18% 58% 24%	χ2  = 32.66**
Birthplace Israel Other	60%  40%	99% 1%	χ2  = 46.66**

*p<0.05

**p<0.01

1. What is the conclusion from the results of the test done between nationality and age? Did a significant correlation had been found? Which test did the researchers use?

2. The Pearson correlation between all the of the research variables is displayed in the following table. Please report (in length) what is the most important correlation. explain why.

Table 2

Correlations Among Variables in Regression Models

Variable	1	2	3	4	5	6	7	8	9	10
1. PTSD	--
2. Depression	.77**	--
3. Somatization	.58**	.66**	--
4. Group	-.38**	-.46 **	-.04	--
5. Age	.03	-.03	.19**	.23**	--
6. Gender	.21**	.23**	.20**	.11	.05	--
7. Education	-.22**	-.23**	-.27**	.16*	.06	-.05	--
8. Religiosity	-.20**	-.21**	-.09	.34**	.10	-.03	-.26**	--
9. Marriage	-.13	-.12	-.09	.14	-.47**	-.04	.05	.15*	--
10. Birthplace	-.15	-.21**	.02	.48**	.45**	.11	.08	.19**	-.07	--

*p<0.05

**p<0.01