Access over 20 million homework & study documents
search

Mathematical Probability Ch 9 Exercises

Content type

User Generated

Subject

Mathematics

Type

Other

Rating

Showing Page:
1/8

Sign up to view the full document!

lock_open Sign Up
Showing Page:
2/8

Sign up to view the full document!

lock_open Sign Up
Showing Page:
3/8

Sign up to view the full document!

lock_open Sign Up
End of Preview - Want to read all 8 pages?
Access Now

Unformatted Attachment Preview

MAT 1600 – Chapter 9 Problem Set 1. Assume that an investor holds a portfolio consisting of 1,000 stocks whose rates of return are normally distributed. A sample of 30 of these stocks is chosen; the sample mean returns is 5%. The sample standard deviation of the return is 8%. a. Contract a 90% confidence interval for the population mean rate of returns Since we have Sample mean and Sample Standard deviation, we use t-Test, using t-table: 90% π‘–π‘›π‘‘π‘’π‘Ÿπ‘£π‘Žπ‘™ β†’ 100(1 βˆ’ 𝛼) = 90% β†’ 𝛼 = 10% = 0.1 𝛼 0.1 = = 0.05 2 2 𝑛 = 30 𝑑 π‘›βˆ’1 𝛼 = 𝑑 29 0.05 = 1.699 2 𝑛 = 30 𝑑𝑓 = 30 βˆ’ 1 = 29 Given: { 𝑠 = 0.08 𝑋̅ = 0.05 𝑋̅ Β± 𝑑 π‘›βˆ’1 𝛼 2 ( 𝑠 0.08 ) = 0.05 Β± (1.699) ( ) = 0.05 Β± 0.0248 βˆšπ‘› √30 = (0.0252, 0.0748) b. Construct a 95% confidence interval for the population mean rate of returns 95% π‘–π‘›π‘‘π‘’π‘Ÿπ‘£π‘Žπ‘™ β†’ 100(1 βˆ’ 𝛼) = 95% β†’ 𝛼 = 5% = 0.05 𝛼 0.05 = = 0.025 2 2 𝑛 = 30 𝑑 π‘›βˆ’1 𝛼 = 𝑑 29 0.025 = 2.045 2 𝑋̅ Β± 𝑑 π‘›βˆ’1 𝛼 2 ( 𝑠 0.08 ) = 0.05 Β± (2.045) ( ) = 0.05 Β± 0.0299 βˆšπ‘› √30 = (0.0201, 0.0799) c. Constructs a 99% confidence interval for the population mean rate of return 99% π‘–π‘›π‘‘π‘’π‘Ÿπ‘£π‘Žπ‘™ β†’ 100(1 βˆ’ 𝛼) = 99% β†’ 𝛼 = 1% = 0.01 𝛼 0.01 = = 0.005 2 2 𝑛 = 30 MAT 1600 – Chapter 9 Problem Set 𝑑 π‘›βˆ’1 𝛼 2 = 𝑑 29 0.005 = 2.756 𝑋̅ Β± 𝑑 π‘›βˆ’1 𝛼 2 ( 𝑠 0.08 ) = 0.0 ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Anonymous
Just the thing I needed, saved me a lot of time.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4