sampling distributions and statistical inferenceA consulting firm was hired to perform a survey on people living in New York City. The survey was completed monthly for six months by 445 randomly-selected people in different boroughs. There were a number of items on the survey, but six basic biographical items will be studied for this exercise. The data for the people surveyed in one of these monthly surveys can be found in the Excel file Survey (attached below). The variables that were used for the basic biographical data are found on the last page of the exercise.
In this exercise, some of the estimation techniques presented in the module will be applied to the New York survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community, and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results.
New York City governmental agency personnel like to have point estimates regarding variables describing the biographical information of the people living within the different boroughs. It is very helpful for them to have some idea regarding the likely accuracy of these estimates as well. Therein lies the benefit of the techniques presented in this module and applied here.
Item A in the description of the data collection instrument lists variables 1–5, which represent the respondent’s general attitude toward each of the five boroughs. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement.
Determine the point estimate, and then construct the 95% confidence interval for µ1= the average attitude toward Manhattan.
Repeat part (a) for µ2 through µ5, the average attitudes toward Brooklyn, Queens, The Bronx and Staten Island, respectively.
Given the breakdown of responses for variable 6 (highest level of education), determine the point estimate, and then construct the 95% confidence interval for p6 = the population proportion of doctoral degrees.
Given the breakdown of responses for variable 7 (marital status of respondent), determine the point estimate, and then construct the 95% confidence interval for p7 = the population proportion in the “single or other” category.
Assume the governmental agencies requested estimates of the mean attitudes towards each borough with a margin of error of 0.05 for each borough. If the governmental agency personnel want to have 95% confidence that the sample mean will fall within this margin of error, how large should the sample sizes be for each borough
Write a report that uses the Written Assignment Requirements under the heading Expectations for CSU-Global Written Assignments found in the CSU-Global Guide to Writing and APA. Items that should be included, at a minimum, are a title page, an introduction, a body that answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment response.
Note: You must submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.
A. General Attitude toward Each Borough (Variables 1–5)
The Bronx 5.
Like Very Much (5) (5) (5) (5) (5)
Like (4) (4) (4) (4) (4)
Neutral (3) (3) (3) (3) (3)
Dislike (2) (2) (2) (2) (2)
Dislike Very Much (1) (1) (1) (1) (1)
B. Information about the Respondent (Variables 6–7)
What is your highest level of education
(1) = Did not complete high school
(2) = High school degree/GED
(3) = Associate’s degree
(4) = Bachelor’s degree
(5) = Master’s degree
(6) = Doctoral degree
Marital Status: (1) = Married, (2) = Single or other
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New York Survey Statistics
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Running xxxxx NEWYORK CITY xxxxxx xxxxxxx 1
xxx York City Survey xxxxxxx
The xxxxxx xx xxxxx the xxxxxx result xx the xxx xxxx City, where xxx xxxxxx people were selected and their likeness xxx noted xxx xxxx different boroughs xx New York xxxxx xxxxx boroughs included the Manhattan, Brooklyn, xxxxxxx The xxxxx and Staten xxxxxxx xxx response was xxxxx xx the xxxxxxxx xx xxx xxxx based on xxx xxxxxxx xxxxx xx measurement. Ordinal scale xxxxxxxx the xxxxxxxx as xxxxxxxx
xxxx very xxxx
xxxxxxx xxxx much
Individual’x xxxxxxx status and education xxxxx xxxx also measured on the xxxxxxx scale xx xxxxxxxxxxx xxxxx included xxx following:
Single or other
xxx xxx complete high xxxxxx
High xxxxxx degree