Problem 1 Let the following sample of 8 observations be drawn from a normal popu

Question

Problem 1 Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 14, 25, 17, 28, 15, 21. Show your work for full credit. 1. (2 pts) Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places. Round "sample mean" to 3 decimal places and "Sample Standard deviation" answer to 2 decimal places) 2. pts) Construct the 90% confidence interval for the population mean. (Round "t value to 3 decimal places and final answers to 2 decimal places.) 3. (3 pts) Construct the 95% confidence interval for the population mean. (Round 't" value to 3 decimal places and final answers to 2 decimal places.)

Explanation / Answer

PROBLEM-1

Part-1

From following calcaultions mean xbar=20 and standard deviation s=4.90

Part-2

degree of freedom =n-1=8-1=7

Critical t at 10% level =1.895

90% confidence interval =Mean-t*s/sqrt(n) , Mean+t*s/sqrt(n)

=20-1.895*4.90/sqrt(8)   20+1.895*4.90/sqrt(8)

=(16.72 23.28)

Part-3

degree of freedom =n-1=8-1=7

Critical t at 5% level =2.365

90% confidence interval =Mean-t*s/sqrt(n) , Mean+t*s/sqrt(n)

=20-2.365*4.90/sqrt(8)   20+2.365*4.90/sqrt(8)

=(15.90 24.10)

S.No x (x-20)^2 1 22 4 2 18 4 3 14 36 4 25 25 5 17 9 6 28 64 7 15 25 8 21 1 Total 160 168 Mean=160/8 20 Variance=168/(8-1) 24 Standard Deviation=sqrt(24) 4.90

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