Statistics Homework Questions - Desklib
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This article contains solutions and answers to Statistics Homework Questions. It covers topics like probability, binomial distribution, population, sample, and more. The output is in tabular and graphical form. The article is relevant to students studying statistics and related courses in colleges and universities.
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Running Head: STATISTICS HOMEWORK QUESTIONS
Statistics Homework Questions
Name of the Student
Name of the University
Author Note
Statistics Homework Questions
Name of the Student
Name of the University
Author Note
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1STATISTICS HOMEWORK QUESTIONS
Table of Contents
Module 2: Homework Questions...............................................................................................3
Answer 1, Answer 2 and Answer 3........................................................................................3
Answer 4................................................................................................................................3
Answer 5................................................................................................................................3
Answer 9................................................................................................................................4
Answer 10..............................................................................................................................4
Module 3: Homework Questions...............................................................................................5
Answer 1................................................................................................................................5
Answer 2................................................................................................................................5
Answer 3................................................................................................................................5
Answer 4................................................................................................................................6
Answer 5................................................................................................................................6
Answer 6................................................................................................................................7
Answer 7................................................................................................................................7
Answer 8................................................................................................................................8
Answer 9................................................................................................................................8
Answer 10..............................................................................................................................8
Module 4: Homework Questions...............................................................................................9
Answer 1................................................................................................................................9
Answer 2..............................................................................................................................10
Table of Contents
Module 2: Homework Questions...............................................................................................3
Answer 1, Answer 2 and Answer 3........................................................................................3
Answer 4................................................................................................................................3
Answer 5................................................................................................................................3
Answer 9................................................................................................................................4
Answer 10..............................................................................................................................4
Module 3: Homework Questions...............................................................................................5
Answer 1................................................................................................................................5
Answer 2................................................................................................................................5
Answer 3................................................................................................................................5
Answer 4................................................................................................................................6
Answer 5................................................................................................................................6
Answer 6................................................................................................................................7
Answer 7................................................................................................................................7
Answer 8................................................................................................................................8
Answer 9................................................................................................................................8
Answer 10..............................................................................................................................8
Module 4: Homework Questions...............................................................................................9
Answer 1................................................................................................................................9
Answer 2..............................................................................................................................10
2STATISTICS HOMEWORK QUESTIONS
Answer 3..............................................................................................................................10
Answer 4..............................................................................................................................11
Answer 5..............................................................................................................................11
Answer 6..............................................................................................................................11
Answer 7..............................................................................................................................12
Answer 8..............................................................................................................................12
Answer 9..............................................................................................................................13
Answer 10............................................................................................................................13
Answer 3..............................................................................................................................10
Answer 4..............................................................................................................................11
Answer 5..............................................................................................................................11
Answer 6..............................................................................................................................11
Answer 7..............................................................................................................................12
Answer 8..............................................................................................................................12
Answer 9..............................................................................................................................13
Answer 10............................................................................................................................13
3STATISTICS HOMEWORK QUESTIONS
Module 2: Homework Questions
Answer 1, Answer 2 and Answer 3
Time GDP growth (%) Inflation (%) Unemployment (%)
2006 2.98 3.54 4.8
2007 3.76 2.33 4.4
2008 3.71 4.35 4.2
2009 1.82 1.82 5.6
2010 2.02 2.85 5.2
2011 2.38 3.3 5.1
2012 3.63 1.76 5.2
2013 2.44 2.45 5.7
2014 2.5 2.49 6.1
1. Arithmetic Mean 2.80 2.77 5.14
2. Median 2.5 2.49 5.2
3. Standard Deviation 0.74 0.84 0.61
Answer 4
Australia China
Population Growth
(%)
Fuel exports
(%)
Population Growth
(%)
Fuel exports
(%)
Mean 1.56 29.17 0.50 1.70
Median 1.56 29.88 0.50 1.69
Standard
Deviation 0.42 3.15 0.03 0.22
Answer 5
Class Frequency (f) Class Mark (x) xf (x^2)f
50 - 60 1 55 55 3025
Module 2: Homework Questions
Answer 1, Answer 2 and Answer 3
Time GDP growth (%) Inflation (%) Unemployment (%)
2006 2.98 3.54 4.8
2007 3.76 2.33 4.4
2008 3.71 4.35 4.2
2009 1.82 1.82 5.6
2010 2.02 2.85 5.2
2011 2.38 3.3 5.1
2012 3.63 1.76 5.2
2013 2.44 2.45 5.7
2014 2.5 2.49 6.1
1. Arithmetic Mean 2.80 2.77 5.14
2. Median 2.5 2.49 5.2
3. Standard Deviation 0.74 0.84 0.61
Answer 4
Australia China
Population Growth
(%)
Fuel exports
(%)
Population Growth
(%)
Fuel exports
(%)
Mean 1.56 29.17 0.50 1.70
Median 1.56 29.88 0.50 1.69
Standard
Deviation 0.42 3.15 0.03 0.22
Answer 5
Class Frequency (f) Class Mark (x) xf (x^2)f
50 - 60 1 55 55 3025
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4STATISTICS HOMEWORK QUESTIONS
60 - 70 5 65 325 21125
70 - 80 3 75 225 16875
80 - 90 3 85 255 21675
90 - 100 3 95 285 27075
Total 15 1145 89775
Mean 76.33
Standard Deviation 12.58
Answer 9
Population Growth (%)
Australia China
Skewnes
s -1.32 1.43
Kurtosis 2.97 2.49
Answer 10
Population Growth (%)
Australia China
First Quartile 1.48 0.49
Third Quartile 1.72 0.51
60 - 70 5 65 325 21125
70 - 80 3 75 225 16875
80 - 90 3 85 255 21675
90 - 100 3 95 285 27075
Total 15 1145 89775
Mean 76.33
Standard Deviation 12.58
Answer 9
Population Growth (%)
Australia China
Skewnes
s -1.32 1.43
Kurtosis 2.97 2.49
Answer 10
Population Growth (%)
Australia China
First Quartile 1.48 0.49
Third Quartile 1.72 0.51
5STATISTICS HOMEWORK QUESTIONS
Module 3: Homework Questions
Answer 1
P (A) = 0.5
P (B) = 0.3
P (A ∩ B) = 0.1
Therefore, P (A ∪ B) = P (A) + P (B) – P (A ∩ B)
= 0.5 + 0.3 – 0.1
= 0.7
Therefore, P ( A |B )= P( A ∩ B)
P( B) = 0.1
0.3 = 1
3 =0.33
Therefore, P ( B| A ) = P( A ∩ B)
P ( A ) = 0.1
0.5 = 1
5 =0.2
Answer 2
Number of customers hearing on Radio [n (R)] = 40
Number of customers watching on TV [n (T)] = 30
Number of customers knowing from both [n (R ∩ T)] = 20
Number of customers Surveyed = n (R ∪ T)
= n (R) + n (T) – n (R ∩ T)
= 40 + 30 – 20
= 50
Answer 3
Module 3: Homework Questions
Answer 1
P (A) = 0.5
P (B) = 0.3
P (A ∩ B) = 0.1
Therefore, P (A ∪ B) = P (A) + P (B) – P (A ∩ B)
= 0.5 + 0.3 – 0.1
= 0.7
Therefore, P ( A |B )= P( A ∩ B)
P( B) = 0.1
0.3 = 1
3 =0.33
Therefore, P ( B| A ) = P( A ∩ B)
P ( A ) = 0.1
0.5 = 1
5 =0.2
Answer 2
Number of customers hearing on Radio [n (R)] = 40
Number of customers watching on TV [n (T)] = 30
Number of customers knowing from both [n (R ∩ T)] = 20
Number of customers Surveyed = n (R ∪ T)
= n (R) + n (T) – n (R ∩ T)
= 40 + 30 – 20
= 50
Answer 3
6STATISTICS HOMEWORK QUESTIONS
High Growth Stocks High Dividend Stocks Total
Increased in Value 30 10 40
Not Increased in Value 30 30 60
Total 60 40 100
High Growth Stocks High Dividend Stocks Total
Increased in Value 0.3 0.1 0.4
Not Increased in Value 0.3 0.3 0.6
Total 0.6 0.4 1
(a) If a stock is selected at random, the probability that the stock will be a high
dividend that has increased in value is 0.1
(b) The probability of selecting a stock that has not increased in value is 0.6
(c) If the stock selected has increased in value, the probability that it is a high
growth stock is (0.3 / 0.4) = 0.75
Answer 4
P (A) = 0.2
P (B) = 0.1
A and B are independent
(a) Therefore, probability that both jobs will be offered = P (A ∩ B) = P (A) * P
(B) = 0.2 * 0.1 = 0.02
(b) Probability that at least one job will be offered = P (A ∪ B) = P (A) + P (B) =
0.2 + 0.1 = 0.3
(c) Probability that only one job will be offered = P (A ∪ B) – P (A ∩ B) = 0.3 –
0.02 = 0.28
(d) Probability that neither jobs will be offered = 1 – P (A ∪ B) = 1 – 0.3 = 0.7
Answer 5
High Growth Stocks High Dividend Stocks Total
Increased in Value 30 10 40
Not Increased in Value 30 30 60
Total 60 40 100
High Growth Stocks High Dividend Stocks Total
Increased in Value 0.3 0.1 0.4
Not Increased in Value 0.3 0.3 0.6
Total 0.6 0.4 1
(a) If a stock is selected at random, the probability that the stock will be a high
dividend that has increased in value is 0.1
(b) The probability of selecting a stock that has not increased in value is 0.6
(c) If the stock selected has increased in value, the probability that it is a high
growth stock is (0.3 / 0.4) = 0.75
Answer 4
P (A) = 0.2
P (B) = 0.1
A and B are independent
(a) Therefore, probability that both jobs will be offered = P (A ∩ B) = P (A) * P
(B) = 0.2 * 0.1 = 0.02
(b) Probability that at least one job will be offered = P (A ∪ B) = P (A) + P (B) =
0.2 + 0.1 = 0.3
(c) Probability that only one job will be offered = P (A ∪ B) – P (A ∩ B) = 0.3 –
0.02 = 0.28
(d) Probability that neither jobs will be offered = 1 – P (A ∪ B) = 1 – 0.3 = 0.7
Answer 5
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7STATISTICS HOMEWORK QUESTIONS
x (EPS) 2.25 2.5 2.75 3 3.25 3.5 3.75
P(x) 0.05 0.1 0.2 0.25 0.2 0.15 0.05
Mean 3.03
Variance 0.14
Standard Deviation 0.38
Answer 6
Let X denote the number of defective items.
Number of samples drawn = 10
Probability of item being defective = 0.15
X ~ Bin (10, 0.15)
The probability distribution of X is given by the following table:
Number of
Defectives (X) 0 1 2 3 4 5 6 7 8 9 10
P (X = x)
0.19
7
0.34
7
0.27
6
0.13
0
0.04
0
0.00
8
0.00
1
0.00
0
0.00
0
0.00
0
0.00
0
P (X = 3) = 0.130
Probability that three items are defective are 0.130.
Expected Value 1.5
Variance 1.275
Answer 7
Number of Ace
(x) 0 1 2 3 4 5 6 7
P (X = x) 0.2791 0.3907 0.2344 0.0781 0.0156 0.0019 0.0001 0.0000
Probability of getting three aces = 0.0781
Probability of getting four aces = 0.0156
Probability of getting five aces = 0.0019
x (EPS) 2.25 2.5 2.75 3 3.25 3.5 3.75
P(x) 0.05 0.1 0.2 0.25 0.2 0.15 0.05
Mean 3.03
Variance 0.14
Standard Deviation 0.38
Answer 6
Let X denote the number of defective items.
Number of samples drawn = 10
Probability of item being defective = 0.15
X ~ Bin (10, 0.15)
The probability distribution of X is given by the following table:
Number of
Defectives (X) 0 1 2 3 4 5 6 7 8 9 10
P (X = x)
0.19
7
0.34
7
0.27
6
0.13
0
0.04
0
0.00
8
0.00
1
0.00
0
0.00
0
0.00
0
0.00
0
P (X = 3) = 0.130
Probability that three items are defective are 0.130.
Expected Value 1.5
Variance 1.275
Answer 7
Number of Ace
(x) 0 1 2 3 4 5 6 7
P (X = x) 0.2791 0.3907 0.2344 0.0781 0.0156 0.0019 0.0001 0.0000
Probability of getting three aces = 0.0781
Probability of getting four aces = 0.0156
Probability of getting five aces = 0.0019
8STATISTICS HOMEWORK QUESTIONS
Probability of getting six aces = 0.0001
Probability of getting three or more aces =0.0781 + 0.0156 + 0.0019 + 0.0001 = 0.0958
Answer 8
Total number of customers seen in a week = 8
Let the number of customers making a deal = X
Probability of a customer making a deal = 0.2
X ~ Bin (8, 0.2)
Probability that the salesman makes 4 deals after meeting 8 customers = P (X = 4) = 0.0459
Answer 9
Business is Expected Value
Good Bad
Plan A big computer 20000 2000 (20,000 * 0.8) + (2,000 * 0.2) = 16400
Plan B small computer 15000 10000 (15,000 * 0.8) + (10,000 * 0.2) = 14000
Proportions 0.8 0.2
Answer 10
Proportion of people preferring Brand A 0.45
Proportion of people preferring Brand B 0.3
Number of residents selected randomly 10
Let X be the number of residents selected randomly.
X ~ Bin (10, 0.45)
The probability distribution of X is given by:
Number of selected
local residents (X) 0 1 2 3 4 5 6 7 8 9 10
P (X = x)
0.0
025
0.0
207
0.0
763
0.1
665
0.2
384
0.2
340
0.1
596
0.0
746
0.0
229
0.0
042
0.0
003
Probability that 5 of these 10 testers will prefer brand A = P (X = 5) = 0.2340
Probability of getting six aces = 0.0001
Probability of getting three or more aces =0.0781 + 0.0156 + 0.0019 + 0.0001 = 0.0958
Answer 8
Total number of customers seen in a week = 8
Let the number of customers making a deal = X
Probability of a customer making a deal = 0.2
X ~ Bin (8, 0.2)
Probability that the salesman makes 4 deals after meeting 8 customers = P (X = 4) = 0.0459
Answer 9
Business is Expected Value
Good Bad
Plan A big computer 20000 2000 (20,000 * 0.8) + (2,000 * 0.2) = 16400
Plan B small computer 15000 10000 (15,000 * 0.8) + (10,000 * 0.2) = 14000
Proportions 0.8 0.2
Answer 10
Proportion of people preferring Brand A 0.45
Proportion of people preferring Brand B 0.3
Number of residents selected randomly 10
Let X be the number of residents selected randomly.
X ~ Bin (10, 0.45)
The probability distribution of X is given by:
Number of selected
local residents (X) 0 1 2 3 4 5 6 7 8 9 10
P (X = x)
0.0
025
0.0
207
0.0
763
0.1
665
0.2
384
0.2
340
0.1
596
0.0
746
0.0
229
0.0
042
0.0
003
Probability that 5 of these 10 testers will prefer brand A = P (X = 5) = 0.2340
9STATISTICS HOMEWORK QUESTIONS
Module 4: Homework Questions
Answer 1
In general, the term “population” indicates the total number of people in a town, in a
region, in a state or in a country and the respective characteristics that the people possess
such as their age, gender, marital status, ethnicity, religion, etc. The definition of the term
“population” in statistics is a little different from the general sense. In statistics, population
indicates all the members of a defined group that a researcher is about to study.
When a part of the population is selected, it is known as a sample. A sample usually
possesses all the characteristics of a population.
Some examples of sample and population are given as follows:
In a study to determine whether smoking causes cancer, the population of interest will
be all people who smoke. It is not possible to conduct a study on all the smoking
people around the globe. Thus, a considerable number of people will be selected from
the total population for the study.
In a study to determine whether high cholesterol is the cause of hepatitis B, the
population of interest will be all the people having hepatitis B. Collecting a data of
this type is not possible and thus sampling is done randomly by selecting a
considerable number of people having high cholesterol levels.
In a study to test the average lifetime of a bulb manufactured by a company, the
targeted population will be all the bulbs manufactured by the company. It is not
possible to light all the bulbs till they die. Then there will be no more bulbs left to sell.
Thus, sampling is conducted for a considerable number of bulbs from all the
manufactured bulbs and their lifetime is measured.
Module 4: Homework Questions
Answer 1
In general, the term “population” indicates the total number of people in a town, in a
region, in a state or in a country and the respective characteristics that the people possess
such as their age, gender, marital status, ethnicity, religion, etc. The definition of the term
“population” in statistics is a little different from the general sense. In statistics, population
indicates all the members of a defined group that a researcher is about to study.
When a part of the population is selected, it is known as a sample. A sample usually
possesses all the characteristics of a population.
Some examples of sample and population are given as follows:
In a study to determine whether smoking causes cancer, the population of interest will
be all people who smoke. It is not possible to conduct a study on all the smoking
people around the globe. Thus, a considerable number of people will be selected from
the total population for the study.
In a study to determine whether high cholesterol is the cause of hepatitis B, the
population of interest will be all the people having hepatitis B. Collecting a data of
this type is not possible and thus sampling is done randomly by selecting a
considerable number of people having high cholesterol levels.
In a study to test the average lifetime of a bulb manufactured by a company, the
targeted population will be all the bulbs manufactured by the company. It is not
possible to light all the bulbs till they die. Then there will be no more bulbs left to sell.
Thus, sampling is conducted for a considerable number of bulbs from all the
manufactured bulbs and their lifetime is measured.
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10STATISTICS HOMEWORK QUESTIONS
To test the relationship between the income of people and the amount spent on health
care of a particular community, the target population will be all the people of that
community and for the purpose of the study, some people from that community will
be selected to conduct the study and make it simpler and less time consuming.
To find out the average marks secured by all the first year college students in
Australia is higher than 50 percent, the targeted population will be the marks secured
by all the first year college students of Australia. For the simplicity of the study,
considerable number of first year students will be selected from some Australian
colleges and then the research will be conducted. This selection is the sample.
Answer 2
Average number of groceries sold in 1 week 478
Average number of groceries sold in 4 weeks 1912
Standard Deviation 17
Number of groceries to be exceeded 495
(a) For 1 week, the probability of sales exceeding 495 0.158655
(b) For 4 weeks, the probability of sales exceeding 495 1
(c) The average number of groceries sold in 1 week is considerably less than that of the
groceries sold in 4 weeks. Thus, there is a difference in the responses in part (a) and part (b).
Answer 3
no college education 0.1
2 years 0.2
4 years 0.3
6 years 0.4
Mean number of years in college (0 * 0.1) + 2 * 0.2) + (4 * 0.3) + (6 * 0.4) = 4
Random sample of 2 is selected from the population.
The sampling distribution:
To test the relationship between the income of people and the amount spent on health
care of a particular community, the target population will be all the people of that
community and for the purpose of the study, some people from that community will
be selected to conduct the study and make it simpler and less time consuming.
To find out the average marks secured by all the first year college students in
Australia is higher than 50 percent, the targeted population will be the marks secured
by all the first year college students of Australia. For the simplicity of the study,
considerable number of first year students will be selected from some Australian
colleges and then the research will be conducted. This selection is the sample.
Answer 2
Average number of groceries sold in 1 week 478
Average number of groceries sold in 4 weeks 1912
Standard Deviation 17
Number of groceries to be exceeded 495
(a) For 1 week, the probability of sales exceeding 495 0.158655
(b) For 4 weeks, the probability of sales exceeding 495 1
(c) The average number of groceries sold in 1 week is considerably less than that of the
groceries sold in 4 weeks. Thus, there is a difference in the responses in part (a) and part (b).
Answer 3
no college education 0.1
2 years 0.2
4 years 0.3
6 years 0.4
Mean number of years in college (0 * 0.1) + 2 * 0.2) + (4 * 0.3) + (6 * 0.4) = 4
Random sample of 2 is selected from the population.
The sampling distribution:
11STATISTICS HOMEWORK QUESTIONS
Mean = np = 2 * 0.3 = 0.6
Standard Deviation = √ p(1− p)
n = √ 0.3 ×0.7
2 =0.324
Answer 4
Average 130
Standard Deviation 42
sample size 36
Weight to exceed 4320
Value of Z 598.5714
Probability 0
Answer 5
Average 950
Standard Deviation 225
sample size 12
Mean of the sample mean life 950
Standard deviation of sample mean 64.95191
Answer 6
Hypotheses
Null Hypothesis H0: μ = 20
Alternative Hypothesis HA: μ <> 20
Test Type Two
Level of significance
alpha α set to: 0.05
Critical Region
Lower Critical Value -1.9600
Upper Critical Value 1.9600
Sample Data
Sample Standard Deviation s 9
Sample Mean x bar 17
Sample Size n 25
Is Pop StDev known? Y/N Y
Standard Error of the Mean 1.8000
z Sample Statistic -1.6667
p-value from the z distribution 0.0478
Mean = np = 2 * 0.3 = 0.6
Standard Deviation = √ p(1− p)
n = √ 0.3 ×0.7
2 =0.324
Answer 4
Average 130
Standard Deviation 42
sample size 36
Weight to exceed 4320
Value of Z 598.5714
Probability 0
Answer 5
Average 950
Standard Deviation 225
sample size 12
Mean of the sample mean life 950
Standard deviation of sample mean 64.95191
Answer 6
Hypotheses
Null Hypothesis H0: μ = 20
Alternative Hypothesis HA: μ <> 20
Test Type Two
Level of significance
alpha α set to: 0.05
Critical Region
Lower Critical Value -1.9600
Upper Critical Value 1.9600
Sample Data
Sample Standard Deviation s 9
Sample Mean x bar 17
Sample Size n 25
Is Pop StDev known? Y/N Y
Standard Error of the Mean 1.8000
z Sample Statistic -1.6667
p-value from the z distribution 0.0478
12STATISTICS HOMEWORK QUESTIONS
Hypothesis test decision:
Reject the Null Hypothesis
Answer 7
Hypotheses
Null Hypothesis H0: μ ≤ 10
Alternative Hypothesis HA: μ > 10
Test Type Upper
Level of significance
alpha α set to: 0.05
Critical Region
Critical Value
1.644
9
Sample Data
Sample Standard Deviation s 3
Sample Mean x bar 12
Sample Size n 25
Is Pop StDev known? Y/N Y
Standard Error of the Mean
0.600
0
z Sample Statistic
3.333
3
p-value from the z distribution
0.000
4
Hypothesis test decision:
Reject the Null Hypothesis
Answer 8
Hypotheses
Null Hypothesis H0: μ ≤ 10
Alternative Hypothesis HA: μ > 10
Test Type Upper
Level of significance
alpha α set to: 0.05
Critical Region
Degrees of Freedom 24
Hypothesis test decision:
Reject the Null Hypothesis
Answer 7
Hypotheses
Null Hypothesis H0: μ ≤ 10
Alternative Hypothesis HA: μ > 10
Test Type Upper
Level of significance
alpha α set to: 0.05
Critical Region
Critical Value
1.644
9
Sample Data
Sample Standard Deviation s 3
Sample Mean x bar 12
Sample Size n 25
Is Pop StDev known? Y/N Y
Standard Error of the Mean
0.600
0
z Sample Statistic
3.333
3
p-value from the z distribution
0.000
4
Hypothesis test decision:
Reject the Null Hypothesis
Answer 8
Hypotheses
Null Hypothesis H0: μ ≤ 10
Alternative Hypothesis HA: μ > 10
Test Type Upper
Level of significance
alpha α set to: 0.05
Critical Region
Degrees of Freedom 24
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13STATISTICS HOMEWORK QUESTIONS
Critical Value 1.7109
Sample Data
Sample Standard Deviation s 3
Sample Mean x bar 12
Sample Size n 25
Is Pop StDev known? Y/N N
Standard Error of the Mean 0.6000
t Sample Statistic 3.3333
p-value from the t distribution 0.0014
Hypothesis test decision:
Reject the Null Hypothesis
Answer 9
Hypotheses
Null Hypothesis H0: μ = 200
Alternative Hypothesis HA: μ <> 200
Test Type Two
Level of significance
alpha α set to: 0.01
Critical Region
Lower Critical Value -2.5758
Upper Critical Value 2.5758
Sample Data
Sample Standard Deviation s 25
Sample Mean x bar 231
Sample Size n 200
Is Pop StDev known? Y/N Y
Standard Error of the Mean 1.7678
z Sample Statistic
17.536
2
p-value from the z distribution 1.0000
Hypothesis test decision:
Fail to reject the Null Hypothesis
Answer 10
Hypotheses
Null Hypothesis H0: μ ≤ 500000
Critical Value 1.7109
Sample Data
Sample Standard Deviation s 3
Sample Mean x bar 12
Sample Size n 25
Is Pop StDev known? Y/N N
Standard Error of the Mean 0.6000
t Sample Statistic 3.3333
p-value from the t distribution 0.0014
Hypothesis test decision:
Reject the Null Hypothesis
Answer 9
Hypotheses
Null Hypothesis H0: μ = 200
Alternative Hypothesis HA: μ <> 200
Test Type Two
Level of significance
alpha α set to: 0.01
Critical Region
Lower Critical Value -2.5758
Upper Critical Value 2.5758
Sample Data
Sample Standard Deviation s 25
Sample Mean x bar 231
Sample Size n 200
Is Pop StDev known? Y/N Y
Standard Error of the Mean 1.7678
z Sample Statistic
17.536
2
p-value from the z distribution 1.0000
Hypothesis test decision:
Fail to reject the Null Hypothesis
Answer 10
Hypotheses
Null Hypothesis H0: μ ≤ 500000
14STATISTICS HOMEWORK QUESTIONS
Alternative Hypothesis HA: μ > 500000
Test Type Upper
Level of significance
alpha α set to: 0.10
Critical Region
Degrees of Freedom 99
Critical Value 1.2902
Sample Data
Sample Standard Deviation s 52000
Sample Mean x bar 525000
Sample Size n 100
Is Pop StDev known? Y/N N
Standard Error of the Mean 5200.0000
t Sample Statistic 4.8077
p-value from the t distribution 0.0000
Hypothesis test decision:
Reject the Null Hypothesis
Alternative Hypothesis HA: μ > 500000
Test Type Upper
Level of significance
alpha α set to: 0.10
Critical Region
Degrees of Freedom 99
Critical Value 1.2902
Sample Data
Sample Standard Deviation s 52000
Sample Mean x bar 525000
Sample Size n 100
Is Pop StDev known? Y/N N
Standard Error of the Mean 5200.0000
t Sample Statistic 4.8077
p-value from the t distribution 0.0000
Hypothesis test decision:
Reject the Null Hypothesis
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