Question

Suppose that we will take a random sample of size n from a population having mean and standard deviation o. For each of the following situations, find the mean, varlance, and standard deviation of the sampling distribution of the sample mean : (a) u = 20.0 = 4, n=32 (Round your answers of "o " and "o, 2 to 4 decimal places.) (b) 4 = 557,0 = 25. n = 138 (Round your answers of "o," and "o 2 to 4 decimal places.) (c) u = 7,0 = 1, n = 6 (Round your answers of "o," and "o, 2 to 4 decimal places.) (d) 4 = 86,0 = 8, n = 1.611 (Round your answers of "o " and " o to 4 decimal places.)

Answer 1

a)#Given

$\mu$=20 $\sigma$ =4 n=32

mean μx̅=

20

sampling variance σ²_x̅=σ²/n=4²/32=0.5

std error=σx̅=σ/√n=

0.7071

#

μx̅	20
σ2x̅	0.5
σx̅	0.7071

b)$\mu$=557 $\sigma$ =0.5 n=138

mean μx=

557

sampling variance σ_x̅²=σ²/n=0.0018

std error=σx̅=σ/√n=

0.0426

#

μx̅	557
σ2x̅	0.0018
σx̅	0.0426

c)$\mu$=7  $\sigma$=0.1 n=6

mean μx=

7

sampling variance σ_x̅²=σ²/n=0.0017

std error=σx̅=σ/√n=

0.0408

#

μx̅	7
σ2x̅	0.0017
σx̅	0.0408

d)$\mu$=86 $\sigma$ =8 n=1611

mean μ=

86

sampling variance σ_x̅²=σ²/n=0.0397

std error=σx̅=σ/√n=

0.1993

#

μx̅	86
σ2x̅	0.0397
σx̅	0.1993