he population is normally distributed with known = 19. From the population, a si
ID: 3129962 • Letter: H
Question
he population is normally distributed with known = 19. From the population, a simple random sample of 24 is drawn. The calculated sample mean is 65.
(a)[5] Construct the 94% confidence interval for the population mean.
(b)[5] Construct the 98% confidence interval for the population mean.
Hint: Round off probabilities and values to 5 decimal places. Refer to some Excel value lookups:
QUESTION 2 (10 points)
We have two independent samples with the following information: n 1 = 9 0 x 1 = 1 5 . 7 s 1 = 4 . 8
n 2 = 7 2 x 2 = 1 4 . 3 s 2 = 3 . 6
Let 1 and 2 be the population means.
(a)[8] At the level of significance = 0.05, use the ztest for H0: 1 2 versus H1: 1 > 2
(b)[2] Justify your use of the zstatistic.
Hint: Round off probabilities and values to 5 decimal places. Refer to some Excel value lookups:
Instructor: Thang Nguyen Section: TOM 30211 Date: 02/16/2016
*
0.950
0.970
0.975
0.990
0.995
NORM.S.INV(*)
1.64485
1.88079
1.95996
2.32635
2.57583
*
0.990
0.980
0.970
0.950
0.900
NORM.S.INV(*)
2.32635
2.05375
1.88079
1.64485
1.28155
*
0.950
0.970
0.975
0.990
0.995
NORM.S.INV(*)
1.64485
1.88079
1.95996
2.32635
2.57583
Explanation / Answer
Ans: Given population standard dev=19, sample size=24 and sample mean=65
a) The 94% confidence interval can be found as:
(65-1.88 * 19/sqrt 24, 65+1.88*19/sqrt 24) = (65-7.30, 65+7.30) = ( 57.7, 72.3)
b) The 98% confidence interval can be found as:
(65 - 2.32 * 19/sqrt 24, 65 + 2.32 *19/sqrt 24) = (65-4.89, 65+ 4.89 ) = (60.11, 69.89)
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