Question

Exam 1

1- Let a Population be { 5,7,9,11,13,15}

Find the sample mean distribution for pairs.

(a)Find the Mean + Standard deviation of your distribution

(2)Sketch The distribution.

(3)Compare the values of the mean and standard deviation of the probability mean distribution and the population.

“ Do not give decimals , give exact values”

Extra credit : Do problem #1 using R

10.33- In each of the following examples,state whether we are sampling from a finite population or a hypothetically infinite population , and describe the population.

a-A personnel manager selects 5 of 20 job applicants for an interview.

b-We weigh a gold nugget three times and use the average we obtain as its weight.

c-We observe how many heads we get in 100 flips of a balanced coin.

d-We select 5 of 25 picture postcards displayed in a store to mail to friends.

e-We observe the gasoline mileage obtained by our car for a period of time estimate the miles per gallon for the car.

10.34- Obtain the probability , by counting , of each possible sample if a random sample of size 2 is taken from

a-A finite population of size 3.

b-A finite population of size 4.

10.35- When we sample from an infinite population , what happens to the standard error of the mean when the sample size is

a-Increased from 30 to 120.

b-Decreased from 245 to 5.

10.36- When we sample from an infinite population , what happens to the standard error of the mean when the sample size is

a-Decreased from 1000 to 10?

b-Increased from 80 to 500

10.37- What is the value of the finite population correction factor when

1-N= 100 and n= 10;

2-N=300 and n=25

3-N=5000 and n=100

Answer 1

a.

5	10	-5	25
7	10	-3	9
9	10	-1	1
11	10	1	1
13	10	3	9
15	10	5	25
			Sum=70

The Mean and Standard deviation of your distribution is obtained in R using the code,

x <- c(5,7,9,11,13,15)
mean (x)
sd (x)

Output:

[1] 10
[1] 3.741657

2) Sketch The distribution.

x <- c(5,7,9,11,13,15)
y <- dnorm(x, mean=10, sd=3.741657)
plot(x,y, type="1", lwd=1,main="Normal Distribution",xlab="X",ylab="Y")

3) The standard deviation of the sample is the  standard deviation of the population divided by the square root of the sample size. Hence the sample standard deviation will be smaller. And the sample mean will be equal to the population mean.

10.33
a. Sampling from a finite population ( Population: 20 job applicants is countable population)
b. Hypothetically infinite population ( The average weight defines the weight of hypothetically infinite population)
c. Sampling from a finite population ( number of outcome in population size 100 flips is a countable process)
d. Sampling from a finite population ( sampling of 5 from 25 picture postcards is countable population)
e. Hypothetically infinite population ( The estimate of the miles per gallon for the car defines the
hypothetically infinite population for mileage)

10.34

a. The possible number of sample of size 2 taken from a finite population of size 3 is,

b.

The possible number of sample of size 2 taken from a finite population of size 4 is,

10.35

The standard error is define as,

Since the standarde error is inversely proportional to the square root of sample size, the standard error will decrease when the sample size incerease.

b.

Since the standard error is inversely proportional to the square root of sample size, the standard error will increase when the sample size decerease.

10.36

a.

Increased 10 times

b.

decreased to two fifth.

10.37

The finite population correction factor is define as,

a. N = 100, n = 10

b. N = 300, n = 25

number of possible sample C3