The US Census Bureau is a powerful agency in the United States that is responsible for providing data to the US government. It produces data which is used to allocate budget resources to different...

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Statistics Project Assignment


The US Census Bureau is a powerful agency in the United States that is responsible for providing data to the US government. It produces data which is used to allocate budget resources to different communities in the United States, and even determine how many Congressional representatives each state in the US is permitted. In order to create a census, the Census Bureau has to send out a large number of census workers across the United States, or send mail to households across the entire United States to get data on all US households. The Census Bureau groups data on households into census tracts, where each census tract has a total population of about 4,000 residents. Census tracts should be divided so that the households in the census tracts share certain characteristics, such as economic status. Even though most tracts are around 4,000 residents, there is some variability, which is the focus of this lab. In practice, census tracts usually have a population between 1,200 and 8,000 people. Guidelines: In this lab, you will do the following. · Calculate the sample size for estimating the average population of the United States' census tracts to within a specified margin of error. · Use the calculated sample size n in order to take simple random samples of the census tracts and calculate confidence intervals to demonstrate that you are consistently within a reasonable margin of error. Data: For this lab, you need to download the uscensuspopbytract.csv dataset, which comes from the US Census. · POP100—the total number of people living in the census tract at the time of the 2010 census Questions: 1. Calculate the true mean ? and true standard deviation ? of the census tract populations based on all the rows in the data file, which has information about all of the census tracts in the United States. Use the formulas or correction factors in your software for the population mean and standard deviation. Each tract has its own population size, but all the tracts combined have an average population size ?, which you calculated above. The bureau wants the ability to create accurate estimates of the average population size ? of its census tracts in the future without having to conduct an expensive full census during a non-census year. Instead, they want to perform population surveys over a sample of the census tracts. They want to ensure their estimate is accurate to within 110 people of the true mean census tract population, with a confidence level of 95%. We will use the current data to make estimates of how large these future samples would need to be to achieve their objectives. 2. What  zc critical value from the normal distribution corresponds to a 95% confidence interval? 3. Using the following formula, where E is the specified maximal margin of error, calculate the sample size n for estimating ? when ? is known. (Round your answer up to the nearest whole number.) 4. In order to convince the bureau that the n you calculated would achieve the right level of accuracy, with the specified level of confidence, create 10 samples, and use the samples to create estimates of the population mean. For each of these, create confidence intervals using the following. Sample mean -margin of error to sample mean+ margin of error Sample Interval Sample 1 …………….<><…………… sample="" 2=""><><…………… sample="" 3=""><><………….. sample="" 4=""><><………….. sample="" 5=""><><………….. sample="" 6=""><><…………. sample="" 7=""><><…………. sample="" 8=""><><………… sample="" 9=""><><………… sample="" 10=""><><……….. 5. about 95% of your confidence intervals should contain the true mean ?, which you calculated above. is this true? discuss. pop100 1912 2170 3373 4386 10766 3668 2891 3081 10435 5675 2894 3320 3804 2902 7826 4736 4815 3325 7882 13166 5055 8331 6861 5173 6831 8011 4302 4305 8397 3715 4230 5065 4487 10632 9131 3832 3412 4799 433 5316 10534 6062 4895 0 3321 4264 1638 4303 3467 2099 1727 2055 4583 2732 6025 5391 8767 7858 7050 3789 5269 4451 7329 3922 8923 8731 1434 7102 2378 2439 1394 2180 1469 3023 4327 1774 2931 1410 3104 2951 2812 1814 2191 2715 1379 3362 5792 6565 3482 4318 2211 3731 5198 3791 6329 6919 7335 3992 3411 6801 3652 3843 4518 7069 4661 4615 6 5 0 3619 2900 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Answered 2 days AfterJun 03, 2021

Answer To: The US Census Bureau is a powerful agency in the United States that is responsible for providing...

Suraj answered on Jun 06 2021
128 Votes
We are given with the US census tact data. There is one variable in the data set given as follows:
POP100—the total number of people living
in the census tract at the time of the 2010 census
1)
The first step is to calculate the population mean and population standard deviation from all the rows of the data set. The mean and standard deviation are calculated with the help of MS-Excel. The output table is given as follows:
Thus, the population mean is 4226.09 and population standard deviation is 1981.87. The population size is 73057.
2)
To calculate the sample size with 95% confidence interval. The critical value is taken from the critical value table of z-distribution. Thus, with 95% confidence level the critical value is given as follows:
Level of significance,
Hence, the critical value is 1.96.
3)
The sample size is calculated by using the following formula:
Now plug the given values in the above formula. We get the desired sample size.
Thus, sample size is 1247.
4)
We have calculated our sample size. Now, we will take 10 simple random samples of size 1247 each and calculate their sample mean and sample standard deviation. Then we calculate the 95% confidence interval of these 10 samples.
Now we will take simple random sample of size 1247 from the whole population using MS-Excel. Then the sample mean and sample standard deviation is calculated and in the last we will...
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