A neighborhood with 12,000 residents on the Eastside of San Antonio, Texas is the target of a Federal grant aimed at improving the quality of life in the geographic area. A neighborhood survey was conducted on the adult population in the target area in June 2013. A random sample comprised of 1,096 residents completed questionnaires. Residents were asked to identify the major problems facing the community. These queries allowed for the testing of the following hypothesis, H1: Personal health issues are seen as the most important issues facing the Eastside community.

  1. Using Table 1, which problems are the most important ones facing the community according to the residents? Support your answer.

From the analysis of the responses given by the respondents, it is evident that the most important (serious) problems facing the community are substance abuse, violence and gang activity. This is based on the analysis of the responses given by the respondents. 69.9% of the respondents agreed that substance abuse is a problem in the area, 14.1% were neutral while only 16.0% disagreed. In terms of violence, it was found out that 58.8% of the respondents agreed that it was a problem in the community while 51.8% agreed that gang activity was a problem in the community.

  1. Which problems are the least important ones facing the community according to the residents? Support your answer.

The least important problems in the community are asthma, obesity and cigarette smoking. From the response, it was found out that 28.1% of the respondents agreed that it was a problem, while 30.1 disagreed. Similarly, 30.6% agreed that obesity was a problem while 34.7% disagreed. Finally, 43.3% of the respondents agreed that cigarette smoking is a problem while 27.6% disagreed.
 

  1. Do you support the research hypothesis? Support your answer.

I do not support the hypothesis. This is because the hypothesis fails to capture the actual situation in this community (Lewis, 2013). From the responses obtained, it can be found out that personal health issues are not the most important for the people in this community.
 

  1. Identify two statistical weaknesses associated with this type of statistical analysis.

There are two statistical weaknesses associated with this statistical analysis. The first problem is that this statistical analysis does not consider individual attributes in determining the reasons behind the responses given. The second weakness is that this type of statistical analysis does not indicate the variation of the attributes leading to the specified responses obtained from the respondents.

  1. For the variables in the SPSS output from the General Social Survey conducted in 2012:
  2. Determine which variable has a distribution most centralized around the mean and why?

From the SPSS analysis, the variable with the distribution most centralized around the mean is ‘highest year of school completed’. This is because the mode and median values are closest to the mean. While the mean is 13.5, the mode is 12.0 and median is 13.0. On further consideration, the standard error of the mean is only 0.07.

  1. Which one has a distribution that is more dispersed around the mean and why?

Family income in constant dollars has a distribution that is more dispersed around the mean. This is because the mode, median and mean are highly dispersed. For instance, while the mode is $51,705 the median is $34,470. Surprising, the mean family income is $48,384. Further, the standard error of the mean is 1,114.84.

  1. Which one has the most normal distribution and why?

The variable with the most normal distribution is ‘age of the respondent’. From the analysis, it is evident that this variable has a kurtosis of -0.84. However, we know from interpretation of kurtosis that kurtosis is used in measuring heaviness portrayed by the tails in a distribution. Similarly, in SAS, normal distribution is identified by the existence of a kurtosis of zero. At the same time, distributions considered extremely non-normal are said to have very negative of positive values of kurtosis. Therefore, the values obtained from the SPSS analysis indicate that ‘age of the respondent’ has a kurtosis value close to zero.

  1. For the number of number of hours spent on e-mail and age of respondent, compute a 95 % confidence interval.

Computing confidence interval at 95% for number of hours spent on e-mail and age of respondent (Lane, 2013).
Unknown Mean = sample mean – (z-score* standard deviation)
Unknown mean for number of hours spent on e-mail: 6.9 +/- (1.96*13.05) = 32.48 or 18.68.
Age of respondent at 95% confidence interval: sample mean – (z-score * standard deviation)
47.9 +/- (1.96 * 3.13) = 54.035 or 41.765
 

  1. What do the confidence intervals indicate?

The confidence intervals calculated indicate that the true means lies between the two unknown means. For instance, at confidence interval of 95%, the actual mean of the number of hours spent on email is between 32 years and 18 years. Similarly, at 95% confidence interval the actual mean of the age of the respondents falls between 54 and 41.

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