Harvard Business School

### Question Description

Can you help me understand this Statistics question?

**Instructions**

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. 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 1–5, 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
*μ*_{1 }= the average attitude toward Manhattan. - Repeat part (a) for
*μ*_{2}through*μ*_{5}, the average attitudes toward Brooklyn, Queens, The Bronx and Staten Island, respectively.

- Determine the point estimate, and then construct the 95% confidence interval for
- Given the breakdown of responses for variable 6 (highest level of education), determine the point estimate, and then construct the 95% confidence interval for
*p*_{6 }= 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
*p*_{7}= 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?

**Paper Requirements**

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 (Links to an external site.). 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)**

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. Informat****ion 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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## Final Answer

Attached.

1

Running head: EDUCATION LEVEL, MARITAL STATUS, AND ATTITUDE TOWARDS NEW YORK STATE

BOROUGHS

Education Level, Marital Status, and Attitude towards New York State Boroughs

Student Name

Name of Institution

2

EDUCATION LEVEL, MARITAL STATUS, AND ATTITUDE TOWARDS NEW YORK STATE BOROUGHS

Education Level, Marital Status, and Attitude towards New York State Boroughs

In this data analysis exercise, the average attitude toward five New York boroughs and

the population distribution across the highest education level and marital status categories were

estimated using a random sample of 445 respondents. The mean and confidence interval of the

mean were the most appropriate descriptive measures for the attitude variables given their

measurement on an interval scale. From the point estimates presented in Table 1 below, the

respondents had the best attitude towards Brooklyn and Staten Island and the worst attitudes

towards Queens and The Bronx. The average ratings for Brooklyn and Staten Island fell between

Like and Like Very Much while the average rating for Queens and the Bronx fell between

Dislike and Neutral.

Table 1: Mean and Confidence Intervals

Required Sample Size

Boroughs

Mean

Confidence Interval

1,349

Manhattan

3.23

3.15 to 3.32

1,938

Brooklyn

4.44

4.34 to 4.55

1,956

Queens

2.28

2.17 to 2.38

2,851

The Bronx

2.41

2.28 to 2.54

1,821

Staten Island

4.29

4.19 to 4.39

The confidence interval (CI) of the mean, calculated as the point estimate plus and minus

the margin of error, gives the range of values that the population mean is expected to fall in at a

95% confidence level. The margin of error increased as the standard deviation increased;

consequently, the Bronx which had the highest standard deviation in responses had the widest CI

while Manhattan, which had the lowest standard deviation in responses had the narrowest CI.

Standard deviation also influenced the required sample size to achieve a 0.05 margin of error at a

95% level of confidence. Due to its high standard deviation, the sample size required to attain a

0.05 margin of error in the mean of attitudes towards the Bronx was 2,851. The required sample

size for Manhattan responses was lowest at 1,349 due to the small deviation in responses.

3

EDUCATION LEVEL, MARITAL STATUS, AND ATTITUDE TOWARDS NEW YORK STATE BOROUGHS

The variables, highest education level and marital status were measured as categorical

variables; hence, proportions were used to describe the distri...