Each numerical entry must be accurate to the nearest 0.001 Given a sample of siz

Question

Each numerical entry must be accurate to the nearest 0.001 Given a sample of size 150 of the normal random variable Z_4, 4, 5, 7, and a sample of size 150 of the normal random variable Z_8, 3, 2, let X^bar_1 and X^bar_2 denote the averages of the two samples. a. The difference of the averages X^bar_1 - X^bar_2 is a normal random variable with mean mu = ____ and standard deviation sigma = _____. b. The symmetric about the mean 80% confidence interval for X^bar_1 - X^bar_2 has lower bound L = _______ and upper bound U = ______. If our samples yield averages 3.6166 for X^bar_11 and 8.8125 for X^bar_2., the difference in the interval.

Explanation / Answer

Answer:

a).

mean = 4.4-8 = -3.6

standard deviation = sqrt((5.7^2+3.2^2)/2) =4.622

b).

z value for lower bound 1.282

lower bound = -3.6-1.282*4.622/sqrt(150) =-4.084

upper bound = -3.6+1.282*4.622/sqrt(150) =-3.116

The sample mean difference =3.6166-8.8125 =-5.1959

The difference not contains in the interval.

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