Consider the hypothesis test H0: μ1= μ2 against H1: μ1.Suppose that the sample sizes aren1 = 15 and n2 =μ2. Assume thatσ21 = σ22 andthat the data are drawn from normal distributions. Use α =0.05.

(a) Test the hypothesis and find the P-value.

(b) Explain how the test could be conducted with a confidenceinterval.

(c) What is the power of the test in part (a) for a truedifference in means of 3?

(d) Assuming equal sample sizes, what sample size should beused to obtain β = 0.05 if the true difference in means is -2?Assume that α = 0.05.

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Step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: