Question

In: Statistics and Probability

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.

Solutions

Expert Solution

Solution :

Given that,

a) Point estimate = sample mean = = $ 48,240

sample standard deviation = s = $ 2,794

sample size = n = 35

Degrees of freedom = df = n - 1 = 35 - 1 = 34

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,34 = 1.691

Margin of error = E = t/2,df * (s /n)

= 1.691 * ( 2794 / 35)

Margin of error = E = $ 799

The 90% confidence interval estimate of the population mean is,

  ± E  

= $ 48,240  ± $ 799

= ( $ 47,441, $ 49,039 )

b) Margin of error = E = t/2,df * (s /n)

= 1.691 * ( 2794 / 35)

Margin of error = E = $ 799


Related Solutions

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.
Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed. 40  35  ...
Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed. 40  35  44  51  39  39  40  35  44  30  51  40  47 ​(a) Find the sample mean and sample standard deviation. ​(b) Each employee in the sample is given a ​$3000 raise. Find the sample mean and sample standard deviation for the revised data set. ​(c) Each employee in the sample takes a pay cut of ​$2000 from their original salary. Find the sample mean...
. 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...
The ages of adults who reside in a particular community have a mean of 35 years...
The ages of adults who reside in a particular community have a mean of 35 years with a standard deviation of 5 years. (a) According to Tchebysheff's rule, at least ___ proportion of adult residents have an age between 20 and 50 years. (b) According to Tchebysheff's rule, at least ___ proportion of adult residents have an age between 25 and 45 years. (c) According to Tchebysheff's rule, at least ___ proportion of adult residents have an age between 22.5...
Salaries of 35 college graduates who took a statistics course in college have a​ mean, x...
Salaries of 35 college graduates who took a statistics course in college have a​ mean, x overbar​, of $ 64 comma 500. Assuming a standard​ deviation, sigma​, of ​$10 comma 141​, construct a 99​% confidence interval for estimating the population mean mu.
Salaries of 35 college graduates who took a statistics course in college have a​ mean, x...
Salaries of 35 college graduates who took a statistics course in college have a​ mean, x overbarx​, of $66, 200. Assuming a population standard deviation of ​$17,102, construct a 95​% confidence interval for estimating the population meanμ. ​ ​$__________<μ<​$______________ ​(Round to the nearest integer as​ needed.)
8. A researcher claims that more than 35% of U.S. adults have been a victim to...
8. A researcher claims that more than 35% of U.S. adults have been a victim to identity theft. In a random sample of 490 U.S. adults, 192 of them have been a victim to identity theft. a) Is there enough evidence to support the researchers claim at the 1% level of significance? b) Is there enough evidence to support the claim at the 10% level of significance?
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...
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...
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT