Question

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.

Calculate the true mean μ and true standard deviation σ 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. (Round your answer to two decimal places.) μ 4226.09 σ = 1981.88 people people Each tract has its own population size, but all the tracts combined have an average population size μ, which you calculated above The bureau wants the ability to create accurate estimates of the average population size μ 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 (a) what zc critical value from the normal distribution corresponds to a 95% confidence interval? (Round your answer to two decimal places.) 1.96 (b) using the following formula, where E is the specified maximal margin of error, calculate the sample size n for estimating μ when σ is known. (Round your answer up to the nearest whole number.) n1509 people 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 Interval Sample 1 Sample 2 Sample3 Sample 4 Sample5 Sample 6 Sample 7 Sample 8 Sample 9 9 Sample 10

I just need help with the table. I can probably figure it out if you just write out an explanation for how to do the first one or two samples.

Answer 1

Sample	Interval
sample 1	M = 4226.09 Z = 1.96 sM = √(1981.882/10) = 626.73 μ = M ± Z(sM) μ = 4226.09 ± 1.96*626.73 μ = 4226.09 ± 1228.3594 You can be 95% confident that the population mean (μ) falls between 2997.7306 and 5454.4494.

Likewise remaining samples will be calculate.