Question

In: Statistics and Probability

The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages...

The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 52 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493 , respectively. Let ? be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯ . Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 52 counties will be less than $29 million. Report your answer to four decimal places. ?(?⎯⎯⎯<29) P ( x ¯ < 29 ) = Use the CLT again to determine the probability that the mean taxable wages in James' sample of 52 counties will be greater than $26 $ 26 million. Report your answer to four decimal places. ?(?⎯⎯⎯>26) P ( x ¯ > 26 )

Solutions

Expert Solution

µ = 28.29

sd = 33.493

a) n = 52

                        

                         = P(Z < 0.15)

                         = 0.5596

b) n = 52

                        

                         = P(Z > -0.49)

                         = 1 - P(Z < -0.49)

                         = 1 - 0.3121

                         = 0.6879


Related Solutions

The Bureau of Labor and Statistics (BLS) calculates the unemployment rate for the United States. For...
The Bureau of Labor and Statistics (BLS) calculates the unemployment rate for the United States. For June of 2020, they published numbers that were close to the following: Civilian noninstitutional Population = 260 million Labor Force = 160 million Employed = 142 million Unemployed = 18 million Retired = 60 million A- Calculate the unemployment rate and the participation rate for June of 2020 in the US using two decimal places (3 points each). B- The United States have gone...
According to the US Bureau of Labor Statistics, in the United States, the employment rate measures...
According to the US Bureau of Labor Statistics, in the United States, the employment rate measures the number of people who have a job as a percentage of the working age population. In January 2020 the rate was 61.2%. A) Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define what you will classify as a "success" S and what you will classify as a "failure" F as it refers to...
According to the US Bureau of Labor Statistics, in the United States, the employment rate measures...
According to the US Bureau of Labor Statistics, in the United States, the employment rate measures the number of people who have a job as a percentage of the working age population. In January 2020 the rate was 61.2%. A) Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define what you will classify as a "success" S and what you will classify as a "failure" F as it refers to...
According to the US Bureau of Labor Statistics, in the United States, the employment rate measures...
According to the US Bureau of Labor Statistics, in the United States, the employment rate measures the number of people who have a job as a percentage of the working age population. In January 2020 the rate was 61.2%. A) Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define what you will classify as a "success" S and what you will classify as a "failure" F as it refers to...
According to the Bureau of Labor Statistics (BLS), the mean weekly earnings of salary workers in...
According to the Bureau of Labor Statistics (BLS), the mean weekly earnings of salary workers in the United States in 2018 was µ =$870. Assume that the weekly earnings are approximately normally distributed with a standard deviation of σ = $90. If a salary worker is selected at random, what is the probability that his/her weekly earnings exceed $700? What are the weekly earnings for which 95% of salary workers’ earnings are in this range? What is the weekly earning...
PART A In 2011, the Bureau of Labor Statistics (BLS) announced that of all adult Americans,...
PART A In 2011, the Bureau of Labor Statistics (BLS) announced that of all adult Americans, 139.93 million were employed, 13.43 million were unemployed, and 86.39 million were not in the labor force. The adult population is how many million? Enter a number rounded to two decimal places. PART B In 2011, the Bureau of Labor Statistics (BLS) announced that of all adult Americans, 139.13 million were employed, 13.20 million were unemployed, and 86.90 million were not in the labor...
The Bureau of Labor Statistics (BLS) adjusts the numbers from the household survey to estimate the...
The Bureau of Labor Statistics (BLS) adjusts the numbers from the household survey to estimate the employment picture for the entire population. Once the adjustment is made, the BLS uses the figures to generate key employment indicators. The following table presents information from the household surveys conducted for November 2017 and, for purposes of comparison, November 2016. The numbers in the table are listed in thousands. For example, the number of unemployed in the table for November 2017 indicates that...
In the June 2020, the Bureau of Labor Statistics (BLS) announced that they had possibly miscalculated...
In the June 2020, the Bureau of Labor Statistics (BLS) announced that they had possibly miscalculated the official U.S. unemployment rate for the last three months. The BLS said that they "underestimated" the unemployment rate (for March, April, and May) because of how furloughed workers had been classified. What's a furloughed worker, and should they be considered "employed", "unemployed", or "neither"?
The Bureau of Labor Statistics (BLS) reported that 9.6% of adults aged 20 to 24 years...
The Bureau of Labor Statistics (BLS) reported that 9.6% of adults aged 20 to 24 years were unemployed in April 2015. Suppose that Jacqui believes that in her city the unemployment rate is higher than the reported proportion. She determines the unemployment status of 450 randomly selected adults in the given age range. She decides to conduct a z-test for the proportion p of unemployed adults in her town aged 20 to 24 years old. Determine the power to reject...
Based on the criteria used by the Bureau of Labor Statistics (BLS), identify each person’s status...
Based on the criteria used by the Bureau of Labor Statistics (BLS), identify each person’s status as employed, unemployed, “not in the labor force” (if not in the civilian labor force but still part of the adult population), or “not in the adult population” if not in the civilian adult population. Person Status Lorenzo is a 75-year-old professor. He teaches only one or two courses a year, but he's still pursuing an active research agenda. Neha is a 36-year-old autoworker...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT