Consider the hypothesis test H0:1=2H0:μ1=μ2 against H1:1≠2H1:μ1≠μ2 with known standard deviations 1=9σ1=9 and 2=4.σ2=4. Suppose that sample sizes 1=10n1=10 and 2=16n2=16 and that x⎯⎯1=4.8x¯1=4.8 and x⎯⎯2=7.6.x¯2=7.6. Use =0.05.α=0.05.
(a) Test the hypothesis and find the P-value.
(b) What is the power of the test in part (a) for a true difference in means of 3?
(c) Assuming equal sample sizes, what sample size should be used to obtain =0.05β=0.05 if the true difference in means is 3? Assume that =0.05.α=0.05.
(a) The null hypothesis Choose your answer; The null hypothesis _ rejected is notis rejected. The P-value is Enter your answer; The P-value is . Round your answer to three decimal places (e.g. 98.765).
(b) The power is Enter your answer in accordance to the item b) of the question statement . Round your answer to two decimal places (e.g. 98.76).
(c) 1=2=n1=n2= Enter your answer in accordance to the item c) of the question statement . Round your answer up to the nearest integer.