3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and...

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and Y1...Xn independent of each other. Assume that the common population SD σ is known but the two means are not. Consider testing the hypothesis null: μx = μy vs alternative: μx ≠ μy.

d. Assume σ=1 and n=20. How large must δ be for the size 0.01 test to have power at least 0.99?

e. Assume σ=1and δ=0.2. How large must n be for the size 0.01 test to have power at least 0.99?

Expert Solution

Minitab output:

1-Sample Z Test

Testing mean = null (versus not = null)
Calculating power for mean = null + difference
Alpha = 0.01 Assumed standard deviation = 1.4142

Sample
Size Power Difference
20 0.99 1.55019

(e)

Minitab output:

Power and Sample Size

1-Sample Z Test

Testing mean = null (versus not = null)
Calculating power for mean = null + difference
Alpha = 0.01 Assumed standard deviation = 1.4142

Sample Target
Difference Size Power Actual Power
0.2 1202 0.99 0.990025

orchestra answered 1 year ago

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and...

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Question

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and...

Solutions

Expert Solution

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