New York Survey Data: The Most Comprehensive Collection of New York City Data

U1 = the average attitude toward Manhattan. 

The point estimate of U1 is the sample mean itself. In Excel, the sample mean is obtained using the AVERAGE function. The average excel formula is =AVERAGE (number1, [number2],…). Therefore, the point estimate for U1 = 2.894 

The confidence level is obtained using the CONFIDENCE function. The confidence level excel formula is =CONFIDENCE.NORM (alpha, standard_dev, size).The arguments are explained below. 

Alpha – it is the significance level used to calculate the confidence level. The significance level is equal to 1 minus confidence interval. So, alpha = (1-0.95) = 0.05 

Standard_dev – it is the standard deviation of the data range. U1 standard_dev = 0.9468249 

Size – it is the sample size. U1 size = 455 

Therefore, Manhattan confidence level (95%) = 0.088 

U1 confidence interval, 

Point estimate  confidence level = 2.894  0.088 = [2.806, 2.982] 

U2 = the average attitude toward Brooklyn 

Point estimate = 4.396 

Confidence level (95%) = 0.104 

Confidence interval = 4.396  0.104 = [4.292, 4.500] 

U3 = the average attitude toward Queens 

Point estimate = 2.2989 

Confidence level (95%) = 0.1032 

Confidence interval = 2.2989  0.1032 = [2.1957, 2.4021] 

U4 = the average attitude towards The Bronx 

Point estimate = 2.182 

Confidence level (95%) = 0.120 

Confidence interval = 2.182  0.120 = [2.062, 2.302] 

U5 = the average attitude toward Staten Island 

Point estimate = 4.031 

Confidence level (95%) = 0.122 

Confidence interval = 4.031  0.122 = [3.909, 4.153] 

Brooklyn and Staten Island have the highest point estimates (4), it means that the communities have a positive attitude. The Bronx and Queens have the lowest point estimate (2), it means that the communities have a negative attitude. In Manhattan, the community has a neutral attitude since the point estimate is 3.

 = the population proportion of doctoral degrees. 

The point estimate of the highest level of education = 3.9460674. 

The number of doctoral degrees in the sample is obtained using COUNTIF function. The countif excel formula is =COUNTIF (range, criteria). So, the number of doctorate degrees is 29. 

The population proportion of doctoral degrees is obtained by dividing 29 by 445 (the sample size). Therefore,  = (29/445) = 0.065169. 

A 95% confidence interval estimate of  =  1.96  where  = 445. It follows a binomial distribution. 

0.065169  1.96  = 0.065169  0.022933 

95% confidence interval of  = [0.042235, 0.088102] 

The point estimate of the highest level of education is 3.946, which is equal to 4. It means that the majority of the people living in New York City have a bachelor’s degree. The population proportion of doctoral degrees is 0.065. It means that 7% of the people living in New York City have doctoral degrees.

 = the population proportion in the (single and other) category. 

The point estimate of marital status = 1.766292. 

The number of single and other is obtained using COUNTIF function. So, single and other category = 341. 

The population proportion of single and other category is obtained by dividing 341 by 445 (the sample size). Therefore,  = (341/445) = 0.766292. 

A 95% confidence interval estimate of  =  1.96  where  = 445. It follows a binomial distribution. 

0.766292  1.96  = 0.766292  0.03932 

95% confidence interval of  = [0.726972, 0.805612] 

The point estimate of marital status is 1.766, which is equal to 2. It means that a majority of people living in New York City are not married. The population proportion of single and other is 0.766. It means that 77% of people living in New York City are in the single and other category.

The formula for sample size is, 

The significance level is, 

α = 1 – confidence = 1 - 0.95 = 0.05 

The critical value is obtained using NORMSINV function. The normsinv excel formula is: =NORMSINV (probability).The probability is 0.025.Therefore, the critical value is, 

 = the standard deviation for each borough. 

 = 0.05 the margin of error. 

 = required sample size. 

Therefore, the sample size required for borough is, 

Manhattan. 

 = 0.9468249 

 = 1377.563 = 1378 

Brooklyn. 

 = 1.123451 

 = 1939.458 = 1939 

Queens 

 = 1.1102 

 = 1893.976 = 1894 

The Bronx 

 = 1.292961 

 = 2568.875 = 2569 

Staten Island 

 = 1.314814712 

 = 2656.448 = 2656 

References

Hill, R. C., Griffiths, W. E., & Lim, G. C. (2011).  Principles of Econometrics, 4th Edition . New York: Wiley. 

Briand, G., Hill, R. C., & Hill, R. C. (2011).  Using excel for Principles of econometrics . Hoboken, N.J: John Wiley & Sons, Inc.