BSTA001 – BUSINESS STATISTICS
Table of Contents
Life satisfaction is regarded as one of the essential human values. However, in recent years, the positive aspects of welfare and mental health have been emphasized and measured by psychologists. Researchers have argued that traditional conceptualizations of well-being, which focus only on the absence of disease, may not provide a complete picture of a person’s well-being (Diener, 1994). Life satisfaction, which is an individual’s cognitive appraisal of his or her life, is one aspect of positive subjective well-being. Most of the survey has revealed many benefits for individuals with high life satisfaction. A recent longitudinal study of adolescents found that high life satisfaction functions as a buffer against the impact of stressful life events on developing psychopathology (Suldo & Huebner, 2004).
Studies on life satisfaction and other related constructs such as quality of life and subjective well-being have helped clarify how individuals react to different life circumstances, especially stressful ones. Most of the basis on life satisfaction has was accomplished with adults, given that the willingness to act in productive ways regards the primary goals of adulthood. e.g., relationships, being a parent, work, community involvement is linked to one’s satisfaction in those areas of life (Diener et al., 1999). According to some theories, happiness emerges as basic needs are satisfied. However, in modern, individualistic societies where basic needs are met for most citizens, life satisfaction becomes increasingly connected to attaining goals beyond basic needs Cummins et al., (2002). Cummins & Çivitçi, A. (2007) argued that life satisfaction ‘must involve some comparative processes between current experience and internalized standards’ in more politically and economically advantaged circumstances. Because life satisfaction consists of one’s commitment to one’s goals and beliefs concerning the attainability of those goals (Diener et al., 1999), the emerging strength of goals having a connection to relationships, work, and community involvement during adolescence is likely to inspire life satisfaction with multiple psychological meaning. In addition, life satisfaction can be revealed as meaningful during adolescence as advancing cognitive abilities make it possible for adolescents to more accurately assess and predict how well they will fulfill their basic needs (Cummins & Nistico, 2002).
|Satisfaction in employment opportunity||515||1||11||4.68||3.697|
|How safe you feel ( Satisfaction in Safety)||515||1||11||6.18||3.688|
|Satisfaction in the home you live||515||1||11||6.55||3.920|
|Valid N (listwise)||515|
Descriptive statistics above display all results for each variable used to reach conclusions about that same group, divided by measures of variability and central tendency. Criteria of central tendency yield information about the center of a dataset, and standards of variability describe the spread of a dataset.
This question requires running a Chi-square of two variables to test if they are independent of each other. (see table;
|Socio-Economic factors-satisfaction level||Life Satisfaction level||Total|
|High Life Satisfaction||Low Life satisfaction|
|High health satisfaction||38.844||69.975||106.719|
|Low health satisfaction||59.217||106.527||165.744|
THE Chi-square results indicate 274.463> 5.0239 at 95% confidence interval. Therefore, the null hypothesis is rejected, so life satisfaction and socio-economic factors are not independent.
This seeks to identify average life satisfaction among all Australian populations and use the mean to and standard deviation to run a 95% confidence interval. The descriptive statistics of the variables identified in question 1 were;
The population standard deviation of life satisfaction for all Australians is known
as σ =2. The Confidence interval is 1-α= 95%, and the level of significance: α=0.05.
Secondly, calculate the Z-value: Life satisfaction indicates an average of (M = 6.32, SD = 2). Therefore, the 95% confidence interval is calculated as follows;
CI = x ± α [ð/√n
UCL = 6.32 + 1.96√[2/√515] = 6.492735839
LCL = 6.32 – 1.96√[2/√515] = 6.147264161
Therefore, the upper limit of the 95% confidence interval is 6.492735839, which means that the average life satisfaction of all Australians will not be higher than 6.492735839, the lower limit of the 95% confidence interval is 6.147264161, which means that the average life satisfaction of all Australians will not be lower than 6.147264161. With a 95% confidence, the average life satisfaction of all Australians is estimated to be within the internal of 6.147264161and 6.492735839. So, this indicates that all Australians are halfway satisfied in life.
Is there any evidence to suggest that the average life satisfaction has changed at a 5% level of significance?
Step 1: hypothesis setting where the null hypothesis H0 x = 8, while the alternative hypothesis H1 X ≠ 8
Step 2: statistical test: use Z or T? Therefore, Z test since α is given as 2
Step 3: level of significance (α or α/2), which is represented as α/2= 0.025
Step 4: set up the critical value α=0.025, which gives z=1.96 or -1.96. The degree of freedom is denoted as df =∞. Results can be rejected if Reject null hypothesis (Ho) if Z test > 1.96 or Z test< -1.96
Step 5: gather sample data from question one is given as µo=8, x=6.1767, σ=2.
Step 6: calculate test statistics z = x−µo/σ/√n, therefore, z= 6.1767-8/ 2/ √515= 20.6886
Step 7: make the statistical conclusion: in this regard, the null hypothesis was rejected because Z test =-20.6886 < -1.96. We have sufficient evidence to support all Australians’ average life satisfaction levels changed at a 5% level of significance from 8. Hence, the hypothesis testing indicates enough evidence to reject the null hypothesis and conclude that at a 5% significance level, the average life satisfaction level for every Australian has changed from x =8.
In summary, this report intends to analyze the association satisfaction level and life satisfaction. From the results, one can that; safety has the most significant impact on life satisfaction. This can be determined by the mean of Australians, which is not less than 6.147264161. Finally, there is ample evidence that the life satisfaction of Australians has changed 5%. It is recommended that increasing the satisfaction of other factors will improve life satisfaction, and increase safety satisfaction performance is the most prominent. Life satisfaction intends to link how basic needs are fulfilled and how various other goals are considered achievable, with basic-needs fulfillment being more central for individuals living in less advantaged circumstances. There is reason to believe that life satisfaction becomes a significant psychological variable before adulthood, particularly during adolescence.
Çivitçi, A. (2007) The Adaptation of Multidimensional Students’ Life Satisfaction Scale into Turkish: validity and reliability studies, Eurasian Journal of Educational Research, 26, 51-60.
Cummins, R.A. & Nistico, H. (2002) Maintaining Life Satisfaction: the role of positive cognitive bias, Journal of Happiness Studies, 3, 37-69. http://dx.doi.org/10.1023/A:1015678915305
Dew, T. (1996) The Preliminary Development and Validation of a Multidimensional Life Satisfaction Scale for Adolescents. Unpublished Ph.D. thesis, University of South Carolina, Columbia.
Dew, T. & Huebner, E.S. (1994) Adolescents’ Perceived Quality of Life: an exploratory investigation, Journal of School Psychology, 32, 185-199. http://dx.doi.org/10.1016/0022-4405(94)90010-8
Diener, E. (1994) Assessing Subjective Well-Being: progress and opportunities, Social Indicators Research, 31, 103-157. http://dx.doi.org/10.1007/BF01207052
Diener, E. & Diener, M. (1995) Cross-Cultural Correlates of Life Satisfaction and Self-Esteem, Journal of Personality and Social Psychology, 68, 653-663. http://dx.doi.org/10.1037/0022-35188.8.131.523
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