A researcher wants to estimate the average monthly income of individuals in a certain city. A random sample of 20 individuals is selected, and their monthly incomes (in dollars) are recorded as follows: 2,500 2,800 3,000 3,200 3,400 3,500 3,600 3,700 3,800 4,000 4,100 4,200 4,300 4,500 4,600 4,700 4,900 5,000 5,200 5,500 Assuming the incomes are normally distributed, calculate the 90% confidence interval for the average monthly income of individuals in the city.. Please show all the necessary steps and provide your answer with the appropriate interpretation. Hints: • Calculate the sample mean and sample standard deviation. • Determine the critical value (t-value) for a 90% confidence level. • Calculate the margin of error using the critical value and sample standard deviation. • Calculate the lower and upper bounds of the confidence interval using the sample mean and margin of error. • Interpret the confidence interval in the context of the problem. I

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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A researcher wants to estimate the average monthly income of individuals in a certain
city. A random sample of 20 individuals is selected, and their monthly incomes (in
dollars) are recorded as follows:
2,500 2,800 3,000 3,200 3,400
3,500 3,600
4,100 4,200 4,300 4,500 4,600 4,700 4,900
3,700 3,800 4,000
5,000 5,200 5,500
Assuming the incomes are normally distributed, calculate the 90% confidence interval
for the average monthly income of individuals in the city..
Please show all the necessary steps and provide your answer with the appropriate
interpretation.
Hints:
• Calculate the sample mean and sample standard deviation.
. Determine the critical value (t-value) for a 90% confidence level.
• Calculate the margin of error using the critical value and sample standard
deviation.
• Calculate the lower and upper bounds of the confidence interval using the sample
mean and margin of error.
• Interpret the confidence interval in the context of the problem.
I
Transcribed Image Text:A researcher wants to estimate the average monthly income of individuals in a certain city. A random sample of 20 individuals is selected, and their monthly incomes (in dollars) are recorded as follows: 2,500 2,800 3,000 3,200 3,400 3,500 3,600 4,100 4,200 4,300 4,500 4,600 4,700 4,900 3,700 3,800 4,000 5,000 5,200 5,500 Assuming the incomes are normally distributed, calculate the 90% confidence interval for the average monthly income of individuals in the city.. Please show all the necessary steps and provide your answer with the appropriate interpretation. Hints: • Calculate the sample mean and sample standard deviation. . Determine the critical value (t-value) for a 90% confidence level. • Calculate the margin of error using the critical value and sample standard deviation. • Calculate the lower and upper bounds of the confidence interval using the sample mean and margin of error. • Interpret the confidence interval in the context of the problem. I
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