Final Exam Review Problems Math 13 Statistics Summer 2013

Final Exam Review Problems – Math 13 – Statistics – Summer 2013

These problems are due on the day of the final exam.

Name: (Please PRINT)

Problem 1:

(a) Find the following for this data set {9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}

Mean Median: Mode: Range:

(b) Find standard deviation without using calculator for this data set:

{4, -6, 5, -7}

2

22

1

1

x xs

n

n x xs

n n

Problem 2: A couple wants to have three babies for the next three years, only one baby per year

(either boy or girl) and no other possibility.

Create a sample space, i.e. collection of all simple events:

Find the probability that they will have two girls and a boy.

Find the probability that they will have at least one girl.

Find the probability that they will have no more than two boys.

Find the probability that they will have no girls.

Find the probability that they will have between one and three girls.

Problem 3: Quality Control: As a quality control manager in a clothing company you randomly

select 5 shirts from a collection of 2000 shirts that just came to your company from Bangladesh.

You will reject all the shirts of if you find at least one faulty shirt. It is assumed that there are 20

faulty shirts in the lot of 2000 shirts. Find the probability of accepting all the shirts in this lot.

Problem 4: On the day of an important exam such as the SAT, you keep a backup mechanical

pencil in the event one fails so that you may use the other. Given that there is a 95% chance that

a mechanical pencil would work, what are your chances that you would not have to get a third

mechanical pencil at the test center at the expense of your precious exam time?

Problem 5: Permutation and combination: What are your chances of winning the Mega

Millions Lottery? In Mega Millions you pick 5 numbers from 1 to 56 without replacement and 1

number from 1 to 46.

Problem 6:Assume that you are investing $10,000 in one bond. There are two types of bonds

available. The first bond gives you a 7% return with a default rate of 3% and the second bond

gives you a return of 9% with a default rate of 5%. Which one these bonds would you consider

for investing your $10,000 assuming that you want to maximize your profit.

Problem 7: A new drug named CURAIDS that is 60% effective in extending the average life of

an AIDS patient by twenty years. Five randomly selected AIDS patients from Africa are treated

with this new drug. Answer the following questions based on the above information.

(a) Show that the above situation satisfies all four criteria for the Binomial probability

distribution.

(b) (10 points) Fill in the probabilities in the following table. Show your calculations.

x 0 1 2 3 4 5

P(x)

(c) What is the probability that no more than 4 patients are cured? Use results from part (b), do

not do the calculations again.

(d) Find the probability that more than 2 patients or less than or equal to 5 patients are cured.

Use results from part (b), do not do the calculations again.

(e) Find the probability that at least 4 patients are cured. Use results from part (b), do not do the

calculations again.

(f) Find probability that less than 2 or more than 3 patients are cured. Use results from part (b),

do not do the calculations again.

Problem 8: In a city named Dhaka there were 125 drug related crimes over one year period.

Find the probability that on a given day there will be exactly 3 drug related crimes in that city.

UsePoisson distribution. Explain the requirements for Poisson distribution.

( )!

x eP x

x

Problem 9: According to the U.N. report, the average yearly income in Bangladesh is about

$500/year. It is also estimated that the population standard deviation is $100. Find the following

probabilities:

a) If you randomly select a person find the probability that she/he would make between $400 and

$600.

b) If you randomly select 30 persons find the probability that their average yearly income would

be between $400 and $600.

Problem 10: (Normal Distribution)Assume that you are a restaurant owner. The customer

waiting time at your restaurant is normally distributed with an average waiting time of 12

minutes and a standard deviation of 3 minutes. You want to reward (with a free burger) 2% of

the customers who wait the longest amount of time. So what should you tell your customers

about minimum waiting period before they can get a free burger?

Problem 11: In a survey of 200 Hartnell students, it was found that 60 students said that English

was not their first language. Create a 95% confidence interval for true proportion of Hartnell

students whose first language is not English.

Assumptions:

Margin of error:

Graph:

Confidence interval:

Explanation of confidence interval:

Problem 12: Population proportion A Popular TV show named ROOTS that addressed the

black history and culture in the U.S. was very popular in the 1980s. You are curious if the

majority of the population nowadays have heard of this show or know about it. Your research

indicated that 241 people knew about this show out of 495 people you surveyed. Create a 95%

confidence interval for the true population proportion.

Assumptions:

Graph:

Margin of error:

Confidence interval and explanation:

Problem 13: t-distribution: Following table represents the number of hours 10 different

Hartnell College students work per week.

20 35 23 25 38 15 41 33 19 29

It is known that the distribution of the number of hours a HartnellCollege student works has

approximately bell shape. Create a 95% confidence interval for the true mean of the number of

hours per week a HartnellCollege student works.

Assumptions:

Calculations: / 2

x E x E

sE t

n

Graphs:


Problem 14: Assume that the distribution of average yearly salary for Hartnell College

graduates is a bell shaped curve. A random sample of 13 Hartnell College graduates has a mean

salary of $35,000 and a standard deviation of $5,000. Create a 95% confidence interval for the

population standard deviation.

Assumptions:

Calculations: 2 2

2

2 2

1 1

R L

n s n s

Graph:


Problem 15: It is known that in Bangladesh a person makes on the average $75 a month with a

standard deviation of $9. You, as a researcher, are interested in determining if the monthly

average income per person has increased. Therefore, you take a random sample of 100 people

and find that the sample average is $79. If you desire a significance level of 0.05, then state your

conclusion based on the calculations you make.

Assumptions:

Null and Alternative hypotheses:

Calculations: x

z

n

Graph and critical values:

Conclusions:

Problem 16: A Popular TV show named ROOTS that addressed the black history and culture in

the U.S. was very popular in the 1980s. You are curious if the majority (more than 50%) of the

population nowadays have heard of this show or know about it. Your research indicated that 241

people knew about this show out of 495 people you surveyed. What is your conclusion?

Significance level is 0.05.

Assumptions:


Calculations:p̂ p

zpq

n


Conclusion:

Problem 17: Hypothesis Testing: 200 field workers were surveyed and their average yearly

income was $13,700. The population standard deviation for the income distribution of field

workers is assumed to be $4,000. Use the sample data, with 0.05 significance level, and test the

claim that average income for the population of field workers is different from $14,000 per year.

Requirements:

Null and Alternative Hypotheses:

Test Statistic: * xxz

n

Graph and critical regions:

Conclusion:

Problem 18: Hypothesis test: (Matched pair) An exercise program is claimed to be effective in

reducing weight. The following represents the weights of 8 people before and after the exercise

program. Is there sufficient evidence to support the claim that there is a difference in weights

before and after the program? Use a 0.05 significance level.

Before 150 135 191 210 189 123 132 175

After 148 136 172 192 185 120 135 170

Assumptions:

Null and alternative hypotheses:

Calculations:

* ddt

s

n

and degrees of freedom = n – 1

Graphs and critical points:

Conclusion:

Problem 19: Two population proportions inferences: According to the PEW Research Center for

the People & the Press in 2000 approximately 50% of the people surveyed said that the

immigrants strengthen the U.S. with their hard work and talents whereas in 2006 approximately

41% responded similarly. Let us assume that each year the survey was conducted on 2,000

randomly selected adults in the U.S. Based on this information would you conclude that there is

a progressively negative attitude towards immigrants in the U.S.? (Use significance level of 0.05,

i.e. 95% confidence level)

Assumptions:


Calculations:

1 2 1 2*

1 2

1 2 1 21 2

1 2 1 2

ˆ ˆTest Statistic:

ˆ ˆwhere and and and 1

p p p pz

pq pq

n n

x x x xp p p q p

n n n n


Conclusion:

Create a confidence interval:

1 2 1 2 1 2

1 1 2 2/2

1 2

ˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆwhere margin of error:

p p E p p p p E

p q p qE z

n n

Problem 20: A 50-year long study by the British researchers shows that on the average smokers

live 10 years less than the nonsmokers do. You being the curious cat collected some data from a

reliable source and found that 621 smokers had average life span of 77 while 831 nonsmokers

had an average life of 71. You also have the information that the sample standard deviation for

life expectancy for both the smokers and nonsmokers is 10. Based on this information would

you reject the null hypothesis that there is no difference in the average life expectancy between

the smokers and nonsmokers?

Assumptions:


Calculations:

1 2 1 2*

2 2

1 2

1 2

Test Statistic: x x

ts s

n n


Conclusion:

Problem 21: F-distribution: A new drug was tested on treatment population and placebo

population. Test the claim that variances for two populations differ. Significance level is 0.05.

Treatment group: sample size = 17, mean = 23.84, standard deviation = 2.31

Placebo group: sample size = 36, mean = 21.97, standard deviation = 2.01

Assumptions:


Calculations: 2

* 1

2

2

Test Statistic: s

Fs


Conclusion:

Problem 22: Following represents the amount of tips paid for different bills at a restaurant.

Bill (in $) 20 15 39 69 55 72 85 79

Tips (in $) 5 5 8 10 15 10 20 15

(a) Use hypothesis testing to determine whether there is linear correlation between the bill and

the tip paid?

*

21

2

rt

r

n

Degree of freedom (n – 2)

(b) Find the equation of the regression line for the above set of data.

(c) Predict tip for $95.

(d) Predict tip for $72

END OF FINAL EXAM REVIEW

Midterm 1 Review Problems – Math 13 – Statistics – Summer 2013

These problems are due on the day of the midterm.


Problem 1: Identify different levels of measurements for (a) through (d)

(a) Heights of buildings in the city of Salinas

Nominal Ordinal Interval Ratio

(b) Temperature on different days of the year in Salinas


(c) Possible letter grades you may receive in the class


(d) Names of 10 students from the class


(e) Identify different types of sampling and data:

At a buffet they have different types of foods; these are American food, Asian food, Indian food,

and Italian food. You eat two items randomly from each category of food.

Convenience Systematic Stratified Clustering

(f) Determine if the following example represents discrete or continuous data:

Candy store sells candies only in the following amount: 0.2 lbs, 0.4 lbs, 0.6 lbs…

Continuous Discrete

(g) Many students are getting A’s in Mo’s Statistics class. Tom says Mo is a great teacher, while

Jessica says Mo is an easy grader. This situation is called:

Problem 2: Your grade in the class consists of 2 midterms 15% each, homework 10%, project

5%, attendance 10%, and final 30%. Find the weighted mean if your scores are as follows in the

class.

Midterm 1: 85

Midterm 2: 90

Final: 80

Homework: 95

Project: 100

Attendance: 75

Weighted Mean: w x

xw

Problem 3:




{4, -6, 5, -7}

2

22

1

1

x xs

n

n x xs

n n

Problem 4: For the given set of data create a histogram:

{9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}. To find class frequencies, find the number of digits in

each class.

Step 1: Find the class boundaries and frequencies

Classes Frequency Class boundaries

1 2 -------------

3 4 -------------

5 6 -------------

7 8 -------------

9 10 -------------

Step 2: Create a histogram for the above dataset

Problem 5: Assume that you take a random sample of 200 people from Salinas and find that

their average income is $48,000 per year with a standard deviation of $9000:

(a) What can you say about the number of people who make between $25,500 and $70,500 out

of the sample of 200 people?

(b) What can you say about the number of people who make more than $70,500 out of the

sample of 200 people?

(c) Now assume that you are given the additional information that the average yearly earning in

Salinas is Bell shaped. Now what can you say about the number of people who make more than

$57,000 per year? Draw graph and label it.

(d) If the data distribution is bell shaped, then approximately how many people make between

$39,000 and $66,000? Draw graph and label it.

Problem 6:A couple wants to have three babies for the next three years, only one baby per year








Problem 7: Determine whether the following events are independent or dependent:

a) Being African American or any person of color raised in a the poverty stricken part of a big

city and going to college for higher education

b) Growing up in beautiful Pebble beach community and going to college for higher education

c) A randomly selected student from CA community colleges being successful in four year

college and a randomly selected student from MA community colleges being successful in four

year college

Problem 8: Disjoint events?

a) A person being born in the U.S. and the same person being born in Mexico

b) Father having a college degree and the son having a college degree from the same college as

the father did

c) Sunshine and drizzle









Problem 11: Two events A and B are disjoint if P(A and B) = 0. Are the events A and

Bdisjoint? Use the formula P(A or B) = P(A) + P(B) – P(A and B) and find the value of P(A

and B)given thatP(A) = 0.6, P(B) = 0.3, P(A or B) = 0.7

Problem 12:The average income for the city of Salinas is normally distributed with a mean of

$48,000 and a standard deviation of $9,000. Find the z-scores associated with the following

incomes:

Income for Mr. Chris Mickens is $16,000 per year

Income for Ms. Sandra is $90,000 per year

Are the above data outliers? Explain why.

Problem 13:You have the option of buying one car from 5 different types of cars and you may

pick one insurance from 4 different choices. What are total number of ways you can have the car

and insurance combination?

Problem 14:An access code has 6 characters. First four are digits and the last two are alphabets

which are case sensitive. A thief trying to break this code has a probability of success:

Problem 15:A student committee consists of 13 members. They need to elect a president, a vice

president, and a treasurer. How many different ways this can be accomplished?

Problem 16:Age discrimination: Among 13 managers the company laid off 3 oldest managers.

Do you think there was discrimination involved in the process based on your calculations?

Problem 17: Permutation and combination:What are your chances of winning the Mega



Problem 18: In a hiring process at a company 6 top managers were hired by taking into

consideration the diversity of pool of applicants drawn from a community which had at least

80% minority populations. At the end of the hiring process no minority manager was hired from

a pool of 30 applicants which proportionately represented the population of the community. Do

you have enough statistical/mathematical justification to question the integrity of the hiring

process given that at least 80% of the population in that community is minority?

END OF MIDTERM 1 REVIEW

Review Problems – Math 13 – Statistics


Problem 1: Identify different levels of measurements for (a) through (d)

(a) Heights of buildings in the city of Salinas


(b) Temperature on different days of the year in Salinas


(c) Possible letter grades you may receive in the class


(d) Names of 10 students from the class


(e) Identify different types of sampling and data:

At a buffet they have different types of foods; these are American food, Asian food, Indian food,

and Italian food. You eat two items randomly from each category of food.

Convenience Systematic Stratified Clustering

(f) Determine if the following example represents discrete or continuous data:

Candy store sells candies only in the following amount: 0.2 lbs, 0.4 lbs, 0.6 lbs…

Continuous Discrete

(g) Many students are getting A’s in Mo’s Statistics class. Tom says Mo is a great teacher, while

Jessica says Mo is an easy grader. This situation is called:

Problem 2: Your grade in the class consists of 2 midterms 15% each, homework 10%, project

5%, attendance 10%, and final 30%. Find the weighted mean if your scores are as follows in the

class.

Midterm 1: 85

Midterm 2: 90

Final: 80

Homework: 95

Project: 100

Attendance: 75

Weighted Mean: w x

xw

Problem 3:




{4, -6, 5, -7}

2

22

1

1

x xs

n

n x xs

n n

Problem 4: For the given set of data create a histogram:

{9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}. To find class frequencies, find the number of digits in

each class.

Step 1: Find the class boundaries and frequencies

Classes Frequency Class boundaries

1 2 -------------

3 4 -------------

5 6 -------------

7 8 -------------

9 10 -------------

Step 2: Create a histogram for the above dataset

Problem 5: Assume that you take a random sample of 200 people from Salinas and find that

their average income is $48,000 per year with a standard deviation of $9000:

(a) What can you say about the number of people who make between $25,500 and $70,500 out

of the sample of 200 people?

(b) What can you say about the number of people who make more than $70,500 out of the

sample of 200 people?

(c) Now assume that you are given the additional information that the average yearly earning in

Salinas is Bell shaped. Now what can you say about the number of people who make more than

$57,000 per year? Draw graph and label it.

(d) If the data distribution is bell shaped, then approximately how many people make between

$39,000 and $66,000? Draw graph and label it.

Problem: A data set has a Bell shape with a mean of 23 and a standard deviation of 4.

(a) Find the data point that is associated with az-score of -1.85.

(b) Is the data point you found in part (a) an outlier? Explain.

Problem 6:A couple wants to have three babies for the next three years, only one baby per year








Problem 7: Determine whether the following events are independent or dependent:

a) Being African American or any person of color raised in a the poverty stricken part of a big

city and going to college for higher education

b) Growing up in beautiful Pebble beach community and going to college for higher education

c) A randomly selected student from CA community colleges being successful in four year

college and a randomly selected student from MA community colleges being successful in four

year college

Problem 8: Disjoint events?

a) A person being born in the U.S. and the same person being born in Mexico

b) Father having a college degree and the son having a college degree from the same college as

the father did

c) Sunshine and drizzle









Problem 11: Two events A and B are disjoint if P(A and B) = 0. Are the events A and

Bdisjoint? Use the formula P(A or B) = P(A) + P(B) – P(A and B) and find the value of P(A

and B)given thatP(A) = 0.6, P(B) = 0.3, P(A or B) = 0.7

Problem 12:

|

P A and BP B A

P A

In a statistics class the following are the outcomes at the end of the semester:

Passed Failed

Students who expected to pass 35 5

Students who expected to fail 4 15

Find the probability that a randomly selected student passed, given that the student expected to

fail.

Problem 13:You have the option of buying one car from 5 different types of cars and you may

pick one insurance from 4 different choices. What are total number of ways you can have the car

and insurance combination?

Problem 14:An access code has 6 characters. First four are digits and the last two are alphabets

which are case sensitive. A thief trying to break this code has a probability of success:

Problem 15:A student committee consists of 13 members. They need to elect a president, a vice

president, and a treasurer. How many different ways this can be accomplished?

Problem 16:Age discrimination: Among 13 managers the company laid off 3 oldest managers.

Do you think there was discrimination involved in the process based on your calculations?

Problem 17: Permutation and combination:What are your chances of winning the Mega



Problem 18: In a hiring process at a company 6 top managers were hired by taking into

consideration the diversity of pool of applicants drawn from a community which had at least

80% minority populations. At the end of the hiring process no minority manager was hired from

a pool of 30 applicants which proportionately represented the population of the community. Do

you have enough statistical/mathematical justification to question the integrity of the hiring

process given that at least 80% of the population in that community is minority?

Problem 19:Assume that you are investing $10,000 in one bond. There are two types of bonds

available. The first bond gives you a 7% return with a default rate of 3% and the second bond

gives you a return of 9% with a default rate of 5%. Which one these bonds would you consider

for investing your $10,000 assuming that you want to maximize your profit.

Problem 20:A new drug named CURAIDS that is 60% effective in extending the average life of

an AIDS patient by twenty years. Five randomly selected AIDS patients from Africa are treated

with this new drug. Answer the following questions based on the above information.

(a) Show that the above situation satisfies all four criteria for the Binomial probability

distribution.

(b) (10 points) Fill in the probabilities in the following table. Show your calculations.

x 0 1 2 3 4 5

P(x)

(c) What is the probability that no more than 4 patients are cured? Use results from part (b), do

not do the calculations again.

(d) Find the probability that more than 2 patients or less than or equal to 5 patients are cured.

Use results from part (b), do not do the calculations again.

(e) Find the probability that at least 4 patients are cured. Use results from part (b), do not do the

calculations again.

(f) Find probability that less than 2 or more than 3 patients are cured. Use results from part (b),

do not do the calculations again.

Problem 21:In a city named Dhaka there were 125 drug related crimes over one year period.

Find the probability that on a given day there will be exactly 3 drug related crimes in that city.

UsePoisson distribution. Explain the requirements for Poisson distribution.

( )!

x eP x

x

Problem 22: Normal approximation to Binomial Distribution: Assume that the probability of giving birth to a baby boy is 0.5; find the probability of giving

birth to at least 180 boys when a survey was conducted on 300 pregnant women. Draw

appropriate graphs and label the points of interest.

Problem 23: Dr. Mohammed Yunus who won the Nobel Peace prize for promoting micro-

financing/mini-loan (normally under $200 per person) for women around the world, especially in

Bangladesh. In a survey of 1000 people who received micro-financing, 89% said that people

who received micro-financing have benefitted from this innovative program. Given that there is

a 50% chance of success for a micro-finance program, find probability that at least 890 people,

i.e. 89% of 1000 people surveyed would say that micro-financing was beneficial.

Problem 24: According to the U.N. report, the average yearly income in Bangladesh is about

$500/year. It is also estimated that the population standard deviation is $100. Find the following

probabilities:

a) If you randomly select a person find the probability that she/he would make between $400 and

$600.

b) If you randomly select 30 persons find the probability that their average yearly income would

be between $400 and $600.

Problem 25: (Normal Distribution)It is known that the average life for a DVD player is 5.4

years and a standard deviation of 0.94 years. If you want to provide a warranty so that only 2%

of the DVD players will be replaced before the warranty expires, what is the time length of the

warranty? Assume normal distribution.

Problem 26: (Normal Distribution)Assume that you are a restaurant owner. The customer

waiting time at your restaurant is normally distributed with an average waiting time of 12

minutes and a standard deviation of 3 minutes. You want to reward (with a free burger) 2% of

the customers who wait the longest amount of time. So what should you tell your customers

about minimum waiting period before they can get a free burger?

Problem 27:Amounts of nicotine in cigarettes (in general) have a mean of 0.952 grams and a

standard deviation of 0.33 grams. The manufacturers claim that they have reduced the amounts

of nicotine in their cigarettes. You do a survey and find that 50 cigarettes have mean nicotine of

0.893 grams. Assume that the mean and the standard deviation of nicotine in cigarettes have not

changed, based on this information find the probability of randomly selecting 50 cigarettes with

a mean of 0.893 or less. Also based on your calculations, would you agree with the

manufacturer’s claim?

Problem 28: In a survey of 200 Hartnell students, it was found that 60 students said that English

was not their first language. Create a 95% confidence interval for true proportion of Hartnell

students whose first language is not English.

Assumptions:

Margin of error:

Graph:

Confidence interval:

Explanation of confidence interval:

Problem 29: Population proportion A Popular TV show named ROOTS that addressed the

black history and culture in the U.S. was very popular in the 1980s. You are curious if the

majority of the population nowadays have heard of this show or know about it. Your research

indicated that 241 people knew about this show out of 495 people you surveyed. Create a 95%

confidence interval for the true population proportion.

Assumptions:

Graph:

Margin of error:


Problem 30: t-distribution: Following table represents the number of hours 10 different

Hartnell College students work per week.

20 35 23 25 38 15 41 33 19 29

It is known that the distribution of the number of hours a HartnellCollege student works has

approximately bell shape. Create a 95% confidence interval for the true mean of the number of

hours per week a HartnellCollege student works.

Assumptions:

Calculations: / 2

x E x E

sE t

n

Graphs:


Problem 31: Assume that the distribution of average yearly salary for Hartnell College

graduates is a bell shaped curve. A random sample of 13 Hartnell College graduates has a mean

salary of $35,000 and a standard deviation of $5,000. Create a 95% confidence interval for the

population standard deviation.

Assumptions:

Calculations: 2 2

2

2 2

1 1

R L

n s n s

Graph:


Problem 32:It is known that in Bangladesh a person makes on the average $75 a month with a

standard deviation of $9. You, as a researcher, are interested in determining if the monthly

average income per person has increased. Therefore, you take a random sample of 100 people

and find that the sample average is $79. If you desire a significance level of 0.05, then state your

conclusion based on the calculations you make.

Assumptions:


Calculations: x

z

n


P-value:

Conclusions:

Problem 33:A Popular TV show named ROOTS that addressed the black history and culture in

the U.S. was very popular in the 1980s. You are curious if the majority (more than 50%) of the

population nowadays have heard of this show or know about it. Your research indicated that 241

people knew about this show out of 495 people you surveyed. What is your conclusion?

Significance level is 0.05.

Assumptions:


Calculations:p̂ p

zpq

n


P-value:

Conclusion:

Problem 34:Hypothesis Testing: 200 field workers were surveyed and their average yearly

income was $13,700. The population standard deviation for the income distribution of field

workers is assumed to be $4,000. Use the sample data, with 0.05 significance level, and test the

claim that average income for the population of field workers is different from $14,000 per year.

Requirements:

Null and Alternative Hypotheses:

Test Statistic: * xxz

n

Graph and critical regions:

P-value:

Conclusion:

Problem 35:Hypothesis test: (Matched pair) An exercise program is claimed to be effective in

reducing weight. The following represents the weights of 8 people before and after the exercise

program. Is there sufficient evidence to support the claim that there is a difference in weights

before and after the program? Use a 0.05 significance level.

Before 150 135 191 210 189 123 132 175

After 148 136 172 192 185 120 135 170

Assumptions:


Calculations:

* ddt

s

n

and degrees of freedom = n – 1


Conclusion:

Problem 36: Two population proportions inferences: According to the PEW Research Center for

the People & the Press in 2000 approximately 50% of the people surveyed said that the

immigrants strengthen the U.S. with their hard work and talents whereas in 2006 approximately

41% responded similarly. Let us assume that each year the survey was conducted on 2,000

randomly selected adults in the U.S. Based on this information would you conclude that there is

a progressively negative attitude towards immigrants in the U.S.? (Use significance level of 0.05,

i.e. 95% confidence level)

Assumptions:


Calculations:

1 2 1 2*

1 2

1 2 1 21 2

1 2 1 2

ˆ ˆTest Statistic:

ˆ ˆwhere and and and 1

p p p pz

pq pq

n n

x x x xp p p q p

n n n n


Conclusion:

Create a confidence interval:

1 2 1 2 1 2

1 1 2 2/2

1 2

ˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆwhere margin of error:

p p E p p p p E

p q p qE z

n n

Problem 37: A 50-year long study by the British researchers shows that on the average smokers

live 10 years less than the nonsmokers do. You being the curious cat collected some data from a

reliable source and found that 621 smokers had average life span of 77 while 831 nonsmokers

had an average life of 71. You also have the information that the sample standard deviation for

life expectancy for both the smokers and nonsmokers is 10. Based on this information would

you reject the null hypothesis that there is no difference in the average life expectancy between

the smokers and nonsmokers?

Assumptions:


Calculations:

1 2 1 2*

2 2

1 2

1 2

Test Statistic: x x

ts s

n n


Conclusion:

Problem 38: F-distribution: A new drug was tested on treatment population and placebo

population. Test the claim that variances for two populations differ. Significance level is 0.05.

Treatment group: sample size = 17, mean = 23.84, standard deviation = 2.31

Placebo group: sample size = 36, mean = 21.97, standard deviation = 2.01

Assumptions:


Calculations: 2

* 1

2

2

Test Statistic: s

Fs


Conclusion:

Problem 39: Following represents the amount of tips paid for different bills at a restaurant.

Bill (in $) 20 15 39 69 55 72 85 79

Tips (in $) 5 5 8 10 15 10 20 15

(a) Use hypothesis testing to determine whether there is linear correlation between the bill and

the tip paid?

*

21

2

rt

r

n

Degree of freedom (n – 2)

(b) Find the equation of the regression line for the above set of data.

(c) Predict tip for $95.

(d) Predict tip for $72

Problem 40:ANOVA: Use F-distribution

Given below are electricity consumptions for four different cities for five different months. Use

a 0.05 significance level to test the null hypothesis that different cities have the same mean for

electricity consumption.

Jan. May July Oct. Nov

City A: 25 29 41 35 36

City B: 30 24 26 39 34

City C: 41 22 28 41 44

City D: 36 31 43 40 35

Assumptions:


Calculations:

Graphs:

Conclusions:

Documents

Final Exam Review Problems Math 13 Statistics Summer 2013