Question

A 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.

1. 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.
2. 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.
3. 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.
4. 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?

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)

1. 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

Some Data: I just need to know how to do the calculations please!

Manhattan	Brooklyn	Queens	The Bronx	Staten Island	Education	Marital Status
1	5	2	2	5	4	2
2	2	4	3	5	5	2
3	5	1	5	4	4	2
2	5	3	2	5	4	2
2	5	2	1	5	2	2
2	5	1	1	2	5	2
2	5	1	4	4	3	2
2	5	4	3	3	4	2
3	5	1	1	5	4	2

Answer 1