Attached.

Psy 520 Graduate Statistics
Chapter 9
9.7
The sampling distribution of the mean is the mean of the population from which the scores
were sampled

9.8
i.
ii.
iii.

All sample drawn from the population are of same size.
The mean of the sample means is equal to the population mean.
The standard deviation of the sample means is equal to the population standard
𝜎
deviation σ divided by the square root of n, that is √𝑛

9.9
a)
b)
c)
d)

Shape would approximate a normal curve TRUE
Mean would equal the one sample mean FALSE
Shape would approximate the shape of the population FALSE
Compared to the population variability, the variability would be reduced by a factor
equal to the square root of 35 TRUE
e) Mean would equal the population mean TRUE
f) Variability would equal the population variability FALSE

9.13
(a)
Sample size; n = 36
Standard error; SE = 1
From the formulae 𝑆𝐸 =

𝜎
√𝑛

Make Standard deviation the subject of the formula
= 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛; 𝜎 = 𝑆𝐸 × √𝑁
= 1 × √36
=1 × 6
=6

(b)
Sample size; n = 36
Standard error; SE = 2
From the formulae 𝑆𝐸 =

𝜎
√𝑛

Make Standard deviation the subject of the formula
= 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛; 𝜎 = 𝑆𝐸 × √𝑁
= 2 × √36
=2 × 6
= 12

(c)
Sample size; n = 36
Standard error; SE = 5
From the formulae 𝑆𝐸 =

𝜎
√𝑛

Make Standard deviation the subject of the formula
= 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛; 𝜎 = 𝑆𝐸 × √𝑁
= 5 × √36
=5 × 6
= 30

(d)
Sample size; n = 36
Standard error; SE = 100
From the formulae 𝑆𝐸 =

𝜎
√𝑛

Make Standard deviation the subject of the formula
= 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛; 𝜎 = 𝑆𝐸 × √𝑁
= 100 × √36
= 100 × 6
= 600

9.14
The Central limit theorem (CLT) states that if random samples of n observations are drawn
from a population with finite μ and standard deviation σ, then, when n is large, the sampling
distribution of the sample mean is approximately normally distributed with mean μ and
𝜎
standard deviation √𝑛

(a)
At this point, according to central limit theorem, we can say that 144...