Question

A consulting firm was hired to conduct 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. 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 through 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? The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic. o The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment. o The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs. • Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables or graphs.) • A. General Attitude toward Each Borough (Variables 1–5) 1. Manhattan 2. Brooklyn 3. Queens 4. The Bronx 5. Staten Island 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.

Answer 1

The Point estimate of mean is the sample mean itself.

In Excel, the sample mean is calculated by function: AVERAGE. The syntax is: =AVERAGE (number1,number2,...)

the confidence level is obtained using the CONFIDENCE function. The syntax is: =CONFIDENCE. NORM(alpha ,standard_ dev, size)

We shall put alpha=1-0.95=0.05 for calculating the confidence intervals. The confidnce interval for mean is mean +-confidence level.

The standard error is given by;

Hence, the required sample size for each varible should be:

the following table have answer

	MANHATTAN	BROOKLYN	QUEENS	THE BRONX	STATEN ISLAND	EDUCATON	MARITUAL STATUS
ALPHA	0.05	0.05	0.05	0.05	0.05	0.05	O.05
MEAN	2.670	4.530	2.465	2.335	4.094	3.476	1.748
STANDARD DEVIATION	1.064	1.045	1.203	1.371	1.223	1.194	0.434
CONFIDENCE LRVEL 95%	0.099	0.097	0.112	0.127	0.114	0.111	0.040
UPPER CONFIDENCE ERROR	2.768	4.627	2.577	2.462	4.208	3.587	1.789
LOWER CONFIDENT ERROR	2.571	4.433	2.353	2.207	3.981	3.365	1.708
MARGIN ERROR	0.05	0.05	0.05	0.05	0.05	0.05	0.05
ROBOT N	21.276	20.900	24.064	27.429	24.459	23.880	8.689
SAMPLE SIZE REQD,N	453	437	579	752	598	570	76