An economic surveys 31 adults living is Townsburg about their salaries. The mean annual salaries for...

An economic surveys 31 adults living is Townsburg about their salaries. The mean annual salaries for those surveyed was found to be x̄ = $47,782, with a standard deviation of $2,488.

a) Find a 90% confidence interval for the true mean annual salary of adults living in Townsburg.

b) Provide the margin of error of the interval as your answer.

Round your answer to the nearest dollar.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 47,782

Population standard deviation = = 2,488
Sample size = n =31

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 1.645 * ( 2488 / $\sqrt$ 31 )

= 735.08
At 90% confidence interval
is,

- E < < + E
47782 - 735.08 < <47782 + 735.08

47046.92 < < 48517.08

orchestra answered 1 year ago

Next > < Previous

Related Solutions

8) An economic surveys 35 adults living is Townsburg about their salaries. The mean annual salaries...

8) An economic surveys 35 adults living is Townsburg about their salaries. The mean annual salaries for those surveyed was found to be x̄ = $48,240, with a standard deviation of $2,794. a) Find a 90% confidence interval for the true mean annual salary of adults living in Townsburg. b) Provide the margin of error of the interval as your answer. Round your answer to the nearest dollar.

. The Gallup organization periodically polls adults living in the U.S. about their approval or disapproval...

. The Gallup organization periodically polls adults living in the U.S. about their approval or disapproval of the job the President of the U.S. is doing. At the end of President Trump’s first month in office, January 2017, his approval rating was 45%, while at the end of last month, March, 2020, his approval rating was 49%.   For the purpose of this problem, suppose that the sample size was 200 in both months, that each represented a simple random sample...

1. The Gallup organization periodically polls adults living in the U.S. about their approval or disapproval...

1. The Gallup organization periodically polls adults living in the U.S. about their approval or disapproval of the job the President of the U.S. is doing. At the end of President Trump’s first month in office, January 2017, his approval rating was 45%, while at the end of last month, March, 2020, his approval rating was 49%.   For the purpose of this problem, suppose that the sample size was 200 in both months, that each represented a simple random sample...

Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2...

Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than $8000? To decide, you select a random sample of statisticians from each region. The results of each survey are shown to the right. At α=0.10, what should you conclude? Answer A-E Region 1 x1 = $68,300 standard deviation = $8,750 n1 = 47 Region 2 x2 = $63,000 standard deviation = $9,275 n2 = 40 A. What are the alternative and null...

A survey is taken to estimate the mean annual family income for families living in public...

A survey is taken to estimate the mean annual family income for families living in public housing in Chicago. For a random sample of 29 families, the annual incomes (in hundreds of dollars) are as follows: 90 77 100 83 64 78 92 73 122 96 60 85 86 108 70 139 56 94 84 111 93 120 70 92 100 124 59 112 79 a. Construct a box plot of the incomes. What do you predict about the shape...

A Gallup Poll released in December 2010 asked 1019 adults living in the Continental U.S. about...

A Gallup Poll released in December 2010 asked 1019 adults living in the Continental U.S. about their belief in the origin of humans. These results, along with results from a more comprehensive poll from 2001 (that we will assume to be exactly accurate), are summarized in the table below: Response Year: 2010 Year: 2001 Humans Evolved with God guiding (1) 38% 37% Humans evolved but God had no part in the process (2) 16% 12% God created humans in present...

Q5. I recorded the annual salaries of 300 employees of a chain computer stores. The mean...

Q5. I recorded the annual salaries of 300 employees of a chain computer stores. The mean and standard deviation are $28,000 and $3,000. If the data show a bell-shaped curve, a) how many employees receive salaries between $25,000 and $31,000? Answer: 300 x ( ) = ( ) employees. b) how many employees receive salaries between 22,000 and 34,000? Answer: 300 x ( ) = ( ) employees. c) how many between 37,000 and 19,000? Answer: 300 x ( )...

Chicago Families: A survey is taken to estimate the mean annual family income for families living...

Chicago Families: A survey is taken to estimate the mean annual family income for families living in public housing in Chicago. From a random sample of 30 families, the annual incomes (in hundreds of dollars) are as follows 83 90 77 100 83 64 78 92 73 122 96 60 85 86 108 70 139 56 94 84 111 93 120 70 92 100 124 59 112 79 a) Construct and interpret a 95% confidence interval for b) Construct a...

A study estimates the mean annual family income for families living in public housing in Chicago....

A study estimates the mean annual family income for families living in public housing in Chicago. For a random sample of 30 families, the annual incomes (in hundreds of dollars) are here: 133 140 127 150 133 114 128 142 123 172 146 110 135 136 158 120 189 106 144 134 161 143 170 120 142 150 174 109 162 129 (a) Produce appropriate plots and predict on the shape of the population distribu- tion? (b) Find and interpret...

Suppose annual salaries for sales associates from Geoff's Computer Shack have a mean of $32,500 and...

Suppose annual salaries for sales associates from Geoff's Computer Shack have a mean of $32,500 and a standard deviation of $2,500. a. Calculate and interpret the z-score for a sales associate who makes $36,000. b. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500. c. Use the empirical rule to determine the percentage of sales associates with...

Subjects