MATH 1530 CAPSTONE TECHNOLOGY PROJECT             SUMMER 2015

Problem 1: Identify Variable Type.  One of these is a variable that is categorical and one is quantitative.  Consider the different graphs that correspond to each variable type.  Use Minitab to create two different graphs appropriate for each variable’s type.  EXTRA CREDIT if you can resize to fit all of the graphs on one page.

NUCLEAR SAFETY            TALK POLITICS

Problem 2: Sampling. In the survey data, the variable “AGE” is the current age reported by each student.

a. Type the first 10 observations from the column representing the variable AGE into the table below, and use this as your sample data for part (b).  Then calculate the mean age of these first 10 observations and report the value below.

N    1    2    3    4    5    6    7    8    9    10
AGE (yrs)

b.  The mean age of the first 10 students is                  years.   (Type the value into the space provided.)

c.  Identify the type of sampling method you have just used:

d.  Next, select a random sample of size n = 10 (Go to Calc > Random Data > Sample from Columns).  Type the number 10 in the “Number of rows to Sample” slot.  Enter the variable “ID” and “AGE” into the “From columns” slot.  Enter C17-C18 into the “Store samples in” slot.  Record the data for your sample in the table below.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

e.  Calculate and report the mean age for your random sample of 10 students.  The sample mean age is
years.

f.  Identify the type of sampling method you have just used:

g.  REPEAT the random sample selection process three more times.  Calculate and report the mean age for each random sample of 10 students.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

ii)  The sample mean age is                        years.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

iii)  The sample mean age is                        years.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

iv)  The sample mean age is                        years.

h.  Suppose we think of all the students who responded to the survey as a population for the purposes of this problem.  In that case, the population mean age is 21.293.  Discuss (two or more complete sentences) the differences and similarities between 21.293 and the answers you got in (b), (e), and ii), iii), and iv).

Problem 3(h): FLIP A COIN.  Circle the outcome  heads / tails  . If you got ‘heads,’ then do this problem.  (Omit this page/problem if you got ‘tails.’)

Question 10 of the SPRING 2015 survey asked students, “How much money did you spend on your last clothing purchase? (in US dollars)”

a.  Create an appropriate graph to display the distribution of the variable called CLOTHING PURCASE and insert it here.

b.  Which of the following best describes the shape of the distribution? Underline your answer.

Skewed left        Symmetric        Skewed right

c.  Using Minitab, calculate the basic statistics for the data collected on CLOTHING PURCASE.  Copy and paste all of the Minitab output here.

d.  Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of CLOTHING PURCASE.

Which statistic will you use to describe the center of the distribution? (Type name of the statistic here.)

e.  What is the value of that statistic? (Type value here.)

f.  Which statistic(s) will you use to describe the spread of the distribution?

g.  What is (are) the value(s) of that (those) statistic(s)?

h.  Look up the IQR rule on p. 50 in our textbook.  Are there any outliers in this distribution?  If so, what are their values?  How many are there?  Justify your answer.

Problem 3(t): YOU JUST FLIPPED A COIN. If you got ‘tails,’ then do this problem.  (Omit this page/problem if you got ‘heads.’)

Question 12 of the FALL 2014 survey asked students, “Usually, how many hours sleep do you get in a night?”  The data is in    column 14 ‘SLEEP’    of the data file.

a.  Create an appropriate graph to display the distribution of the variable called SLEEP and insert it here.

b.  Which of the following best describes the shape of the distribution? Underline your answer.

Skewed left        Symmetric        Skewed right

c.  Using Minitab, calculate the basic statistics for the data collected on SLEEP and copy & paste the Minitab output here.

d.  Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of SLEEP.

i)  Which statistic will you use to describe the center of the distribution? (Type name of the statistic here.)

ii)  What is the value of that statistic? (Type value here.)

iii)  Which statistic(s) will you use to describe the spread of the distribution?

iv)  What is (are) the value(s) of that (those) statistic(s)?

v)  Look up the IQR rule on p. 50 in our textbook.  Are there any outliers in this distribution?  If so, what are their values?  How many are there?  Justify your answer.

Problem 4: Age versus Handwashing.  It is not surprising to see a fairly strong association between certain variables and age.  On the SPRING 2015 Math 1530 survey, questions 3 and 7 asked students to give their age in years (AGE, yrs) and an estimate of how many times each day they wash their hands (WASH HANDS).  We are specifically interested in seeing whether we can use a student’s age to predict daily hand washes.

a.  Create an appropriate graph to display the relationship between AGE and WASH HANDS.  Insert it here.

b.  Does the plot show a positive association, a negative association, or no association between these two variables?  EXPLAIN what this means with respect to the variables being studied.

c.  Describe the form of the relationship between AGE and WASH HANDS.

d.  Report the value of the correlation between this pair of variables?     r =

e.  Based on the information displayed in the graph and the correlation you just reported, how would you describe the strength of the association?

f.  Using Minitab, obtain the equation for the least squares regression of WASH HANDS on AGE.  Copy & paste the output here.

g.  Interpret the value of the slope in the least squares regression equation you found in part (f).

h.  Use the regression equation in part (f) to predict daily hand washes for a student who is 20 years old.  (Show your math.)

Predicted hand washes =

i.  How well does the regression equation fit the data?  Explain.  Justify your answer with appropriate plot(s) and summary statistics.

Question 5 (both)    FLIP A COIN TWICE.    Circle the outcome  of each toss:  1 heads/tails;2 heads/tails.
If you got heads both times or tails both times, then do this problem.  (Omit this page/problem if you got one of each.)

POLITICAL PARTY AND GENDER Question 5 from the FALL 2014 Math 1530 survey asked students “What political party do you identify with?” and Question 2 from that survey asked students “What is your gender?”   The answers to these questions can be found in    column 12 ‘PARTY’    and    column 10 ‘GENDER’    in the Summer 2015 Capstone Data file.  We want to check if there is a relationship between political party and gender among ETSU students.  Assume the students who took the (Fall 2014 Math 1530) class survey are from an SRS of ETSU students.

a.  Create an appropriate graph to display the relationship between POLITICAL PARTY and GENDER.  You don’t want to display information for students that didn’t answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside “Include missing as a group” and “Include empty cells.”  Insert your graph here.

b.  Create an appropriate two-way table to summarize the data.  Click on Options > Display missing values for… and put a dot in the circle beside “No variables.”  Insert your table here.

SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.)

c.  What is the probability that this student is both a male and Republican?

P =

d.  What is the probability that this student is either a female or Independent?

P =

e.  What is the probability that this student is a Democrat given that the student selected is a female?

P =

f.  What is the probability that this student is a female given that the student is a Democrat?

P =

g.  Do you think there may be an association between GENDER and POLITICAL PARTY?  Why or why not?  Explain your reasoning based on what you see in your graph.

Problem 5(mixed): YOU JUST FLIPPED A COIN TWICE. If you got one heads and one tails, then do this problem.  (Omit this page/problem if you got two heads or two tails.)

MARRIED AND DEATH_PENALTY  Question 3 from the FALL 2014 Math 1530 survey asked students “What is your opinion about a married person having sexual relations with someone other than the marriage partner?” and Question 8 from the survey asked students “Do you favor or oppose the death penalty for persons convicted of murder?”  The answers to these questions can be found in    column 11 ‘MARRIED’    and    column 13 ‘DEATH_PENALTY’    in the Summer 2015 Capstone Data file.  We want to check if there is a relationship between MARRIED and DEATH_PENALTY among ETSU students.  Assume the students who took the (Fall 2014 Math 1530) class survey are from an SRS of ETSU students.

a.  Create an appropriate graph to display the relationship between MARRIED and DEATH_PENALTY.  You don’t want to display information for students that didn’t answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside “Include missing as a group” and “Include empty cells.”  Insert your graph here.

b.  Create an appropriate two-way table to summarize the data.  Click on Options > Display missing values for… and put a dot in the circle beside “No variables.”  Insert your table here.

SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.)

c.  What is the probability that this student is both opposed to the Death Penalty and says that sex with someone other than a marriage partner is ‘not wrong at all’?

P =

d.  What is the probability that this student favors the Death Penalty or says that sex with someone other than the marriage partner is ‘always wrong’?

P =

e.  What is the probability that this student is favors the death penalty given that the student says sex with someone other than the marriage partner is ’always wrong’?

P =
f.  What is the probability that this student says that sex with someone other than the marriage partner is ‘always wrong’ given that the student favors the death penalty?

P =

g.  Do you think there may be an association between DEATH PENALTY and MARRIED?  Why or why not?  Explain your reasoning based on what you see in your graph.

Problem 6  The Statistic Brain Research Institute says that the average consumer spends about $59/month on women’s clothes.  http://www.statisticbrain.com/what-consumers-spend-each-month/   Do female ETSU students spend similar amounts on clothing?

Spring 2015 Math 1530 survey question 10 asked     “How much money did you spend on your last clothing purchase? (in US dollars) “    We want data on just the female students.  Minitab will separate the CLOTHING_PURCHASE data into two columns.  Data > Unstack columns >

Unstack the data in:  CLOTHING PURCHASE, GENDER            Using subscripts in:  GENDER

And you get a new worksheet, with the female clothing purchase data in its own column.

a.  Create a suitable graph to display the distribution of CLOTHING_PURCHASE  reported by our sample of female college students and insert it here.

b.  Describe the distribution shown in your graph.

c.  Perform a test of significance to see if female college students have clothing spending habits similar to the average consumer.  If this claim is true, then the average CLOTHING_PURCHASE reported by female students should be $59.  For this test, the null hypothesis is that the average CLOTHING_PURCHASE reported by female students is the what is reported for the average consumer. Thus,

Ho: µ = $59 per month

Write the correct alternative hypothesis for the test.

Ha:

d. Use Minitab to perform the appropriate test.  Copy and paste the output for the test here.

e. What is the name of your test statistic and what is its value?

f. What is the P-value for the test?  P =

g. State your decision regarding the hypothesis being tested.

h. State your conclusion (words about females and clothing.  USE COMPLETE SENTENCES.

i.  Is the P-value valid in this case?  What assumptions are you making in order to carry out this test?

Bonus Problem:  Population males.   According to the Census Bureau,  http://quickfacts.census.gov/qfd/states/00000.html , in 2013, about 49.2.8% of the US population was male.  Is the same true for the population of students at U.S. colleges and universities?   On the Fall 2014 1530 Survey, question #1  asked our Math-1530 students,  “What is your gender? (Female, Male)”   In the data worksheet, we call this variable GENDER the one in column 10.

a.  Create an appropriate graph to display the distribution of GENDER and insert it here.

b.  How many of the students surveyed said “male?”

c.  What proportion of our sample said “male?”

d.  Assume (for the purpose of this problem) that we may treat the Fall 2014 sample of Math-1530 students as a simple random sample drawn from the population of all U.S. college/university students.  Use Minitab to calculate a 95% confidence interval for the proportion of students in the population who would say “male” to the survey question (based on our sample data).  Copy and paste the Minitab output here.

e.  Interpret the confidence interval you reported in part (d).

f.  What do you think?  Do our results contradict the claim made at the Census website or do they appear to agree with it?  EXPLAIN.

MATH 1530 CAPSTONE TECHNOLOGY PROJECT             SUMMER 2015

Problem 1: Identify Variable Type.  One of these is a variable that is categorical and one is quantitative.  Consider the different graphs that correspond to each variable type.  Use Minitab to create two different graphs appropriate for each variable’s type.  EXTRA CREDIT if you can resize to fit all of the graphs on one page.

NUCLEAR SAFETY            TALK POLITICS

Problem 2: Sampling. In the survey data, the variable “AGE” is the current age reported by each student.

a. Type the first 10 observations from the column representing the variable AGE into the table below, and use this as your sample data for part (b).  Then calculate the mean age of these first 10 observations and report the value below.

N    1    2    3    4    5    6    7    8    9    10
AGE (yrs)

b.  The mean age of the first 10 students is                  years.   (Type the value into the space provided.)

c.  Identify the type of sampling method you have just used:

d.  Next, select a random sample of size n = 10 (Go to Calc > Random Data > Sample from Columns).  Type the number 10 in the “Number of rows to Sample” slot.  Enter the variable “ID” and “AGE” into the “From columns” slot.  Enter C17-C18 into the “Store samples in” slot.  Record the data for your sample in the table below.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

e.  Calculate and report the mean age for your random sample of 10 students.  The sample mean age is
years.

f.  Identify the type of sampling method you have just used:

g.  REPEAT the random sample selection process three more times.  Calculate and report the mean age for each random sample of 10 students.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

ii)  The sample mean age is                        years.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

iii)  The sample mean age is                        years.

N    1    2    3    4    5    6    7    8    9    10
ID
AGE (yrs)

iv)  The sample mean age is                        years.

h.  Suppose we think of all the students who responded to the survey as a population for the purposes of this problem.  In that case, the population mean age is 21.293.  Discuss (two or more complete sentences) the differences and similarities between 21.293 and the answers you got in (b), (e), and ii), iii), and iv).

Problem 3(h): FLIP A COIN.  Circle the outcome  heads / tails  . If you got ‘heads,’ then do this problem.  (Omit this page/problem if you got ‘tails.’)

Question 10 of the SPRING 2015 survey asked students, “How much money did you spend on your last clothing purchase? (in US dollars)”

a.  Create an appropriate graph to display the distribution of the variable called CLOTHING PURCASE and insert it here.

b.  Which of the following best describes the shape of the distribution? Underline your answer.

Skewed left        Symmetric        Skewed right

c.  Using Minitab, calculate the basic statistics for the data collected on CLOTHING PURCASE.  Copy and paste all of the Minitab output here.

d.  Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of CLOTHING PURCASE.

Which statistic will you use to describe the center of the distribution? (Type name of the statistic here.)

e.  What is the value of that statistic? (Type value here.)

f.  Which statistic(s) will you use to describe the spread of the distribution?

g.  What is (are) the value(s) of that (those) statistic(s)?

h.  Look up the IQR rule on p. 50 in our textbook.  Are there any outliers in this distribution?  If so, what are their values?  How many are there?  Justify your answer.

Problem 3(t): YOU JUST FLIPPED A COIN. If you got ‘tails,’ then do this problem.  (Omit this page/problem if you got ‘heads.’)

Question 12 of the FALL 2014 survey asked students, “Usually, how many hours sleep do you get in a night?”  The data is in    column 14 ‘SLEEP’    of the data file.

a.  Create an appropriate graph to display the distribution of the variable called SLEEP and insert it here.

b.  Which of the following best describes the shape of the distribution? Underline your answer.

Skewed left        Symmetric        Skewed right

c.  Using Minitab, calculate the basic statistics for the data collected on SLEEP and copy & paste the Minitab output here.

d.  Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of SLEEP.

i)  Which statistic will you use to describe the center of the distribution? (Type name of the statistic here.)

ii)  What is the value of that statistic? (Type value here.)

iii)  Which statistic(s) will you use to describe the spread of the distribution?

iv)  What is (are) the value(s) of that (those) statistic(s)?

v)  Look up the IQR rule on p. 50 in our textbook.  Are there any outliers in this distribution?  If so, what are their values?  How many are there?  Justify your answer.

Problem 4: Age versus Handwashing.  It is not surprising to see a fairly strong association between certain variables and age.  On the SPRING 2015 Math 1530 survey, questions 3 and 7 asked students to give their age in years (AGE, yrs) and an estimate of how many times each day they wash their hands (WASH HANDS).  We are specifically interested in seeing whether we can use a student’s age to predict daily hand washes.

a.  Create an appropriate graph to display the relationship between AGE and WASH HANDS.  Insert it here.

b.  Does the plot show a positive association, a negative association, or no association between these two variables?  EXPLAIN what this means with respect to the variables being studied.

c.  Describe the form of the relationship between AGE and WASH HANDS.

d.  Report the value of the correlation between this pair of variables?     r =

e.  Based on the information displayed in the graph and the correlation you just reported, how would you describe the strength of the association?

f.  Using Minitab, obtain the equation for the least squares regression of WASH HANDS on AGE.  Copy & paste the output here.

g.  Interpret the value of the slope in the least squares regression equation you found in part (f).

h.  Use the regression equation in part (f) to predict daily hand washes for a student who is 20 years old.  (Show your math.)

Predicted hand washes =

i.  How well does the regression equation fit the data?  Explain.  Justify your answer with appropriate plot(s) and summary statistics.

Question 5 (both)    FLIP A COIN TWICE.    Circle the outcome  of each toss:  1 heads/tails;2 heads/tails.
If you got heads both times or tails both times, then do this problem.  (Omit this page/problem if you got one of each.)

POLITICAL PARTY AND GENDER Question 5 from the FALL 2014 Math 1530 survey asked students “What political party do you identify with?” and Question 2 from that survey asked students “What is your gender?”   The answers to these questions can be found in    column 12 ‘PARTY’    and    column 10 ‘GENDER’    in the Summer 2015 Capstone Data file.  We want to check if there is a relationship between political party and gender among ETSU students.  Assume the students who took the (Fall 2014 Math 1530) class survey are from an SRS of ETSU students.

a.  Create an appropriate graph to display the relationship between POLITICAL PARTY and GENDER.  You don’t want to display information for students that didn’t answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside “Include missing as a group” and “Include empty cells.”  Insert your graph here.

b.  Create an appropriate two-way table to summarize the data.  Click on Options > Display missing values for… and put a dot in the circle beside “No variables.”  Insert your table here.

SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.)

c.  What is the probability that this student is both a male and Republican?

P =

d.  What is the probability that this student is either a female or Independent?

P =

e.  What is the probability that this student is a Democrat given that the student selected is a female?

P =

f.  What is the probability that this student is a female given that the student is a Democrat?

P =

g.  Do you think there may be an association between GENDER and POLITICAL PARTY?  Why or why not?  Explain your reasoning based on what you see in your graph.

Problem 5(mixed): YOU JUST FLIPPED A COIN TWICE. If you got one heads and one tails, then do this problem.  (Omit this page/problem if you got two heads or two tails.)

MARRIED AND DEATH_PENALTY  Question 3 from the FALL 2014 Math 1530 survey asked students “What is your opinion about a married person having sexual relations with someone other than the marriage partner?” and Question 8 from the survey asked students “Do you favor or oppose the death penalty for persons convicted of murder?”  The answers to these questions can be found in    column 11 ‘MARRIED’    and    column 13 ‘DEATH_PENALTY’    in the Summer 2015 Capstone Data file.  We want to check if there is a relationship between MARRIED and DEATH_PENALTY among ETSU students.  Assume the students who took the (Fall 2014 Math 1530) class survey are from an SRS of ETSU students.

a.  Create an appropriate graph to display the relationship between MARRIED and DEATH_PENALTY.  You don’t want to display information for students that didn’t answer both of these questions on the survey, so click on Data Options > Group Options and remove the checks in the boxes beside “Include missing as a group” and “Include empty cells.”  Insert your graph here.

b.  Create an appropriate two-way table to summarize the data.  Click on Options > Display missing values for… and put a dot in the circle beside “No variables.”  Insert your table here.

SUPPOSE WE SELECT ONE STUDENT AT RANDOM: (Calculate the following probabilities and show your work.)

c.  What is the probability that this student is both opposed to the Death Penalty and says that sex with someone other than a marriage partner is ‘not wrong at all’?

P =

d.  What is the probability that this student favors the Death Penalty or says that sex with someone other than the marriage partner is ‘always wrong’?

P =

e.  What is the probability that this student is favors the death penalty given that the student says sex with someone other than the marriage partner is ’always wrong’?

P =
f.  What is the probability that this student says that sex with someone other than the marriage partner is ‘always wrong’ given that the student favors the death penalty?

P =

g.  Do you think there may be an association between DEATH PENALTY and MARRIED?  Why or why not?  Explain your reasoning based on what you see in your graph.

Problem 6  The Statistic Brain Research Institute says that the average consumer spends about $59/month on women’s clothes.  http://www.statisticbrain.com/what-consumers-spend-each-month/   Do female ETSU students spend similar amounts on clothing?

Spring 2015 Math 1530 survey question 10 asked     “How much money did you spend on your last clothing purchase? (in US dollars) “    We want data on just the female students.  Minitab will separate the CLOTHING_PURCHASE data into two columns.  Data > Unstack columns >

Unstack the data in:  CLOTHING PURCHASE, GENDER            Using subscripts in:  GENDER

And you get a new worksheet, with the female clothing purchase data in its own column.

a.  Create a suitable graph to display the distribution of CLOTHING_PURCHASE  reported by our sample of female college students and insert it here.

b.  Describe the distribution shown in your graph.

c.  Perform a test of significance to see if female college students have clothing spending habits similar to the average consumer.  If this claim is true, then the average CLOTHING_PURCHASE reported by female students should be $59.  For this test, the null hypothesis is that the average CLOTHING_PURCHASE reported by female students is the what is reported for the average consumer. Thus,

Ho: µ = $59 per month

Write the correct alternative hypothesis for the test.

Ha:

d. Use Minitab to perform the appropriate test.  Copy and paste the output for the test here.

e. What is the name of your test statistic and what is its value?

f. What is the P-value for the test?  P =

g. State your decision regarding the hypothesis being tested.

h. State your conclusion (words about females and clothing.  USE COMPLETE SENTENCES.

i.  Is the P-value valid in this case?  What assumptions are you making in order to carry out this test?

Bonus Problem:  Population males.   According to the Census Bureau,  http://quickfacts.census.gov/qfd/states/00000.html , in 2013, about 49.2.8% of the US population was male.  Is the same true for the population of students at U.S. colleges and universities?   On the Fall 2014 1530 Survey, question #1  asked our Math-1530 students,  “What is your gender? (Female, Male)”   In the data worksheet, we call this variable GENDER the one in column 10.

a.  Create an appropriate graph to display the distribution of GENDER and insert it here.

b.  How many of the students surveyed said “male?”

c.  What proportion of our sample said “male?”

d.  Assume (for the purpose of this problem) that we may treat the Fall 2014 sample of Math-1530 students as a simple random sample drawn from the population of all U.S. college/university students.  Use Minitab to calculate a 95% confidence interval for the proportion of students in the population who would say “male” to the survey question (based on our sample data).  Copy and paste the Minitab output here.

e.  Interpret the confidence interval you reported in part (d).

f.  What do you think?  Do our results contradict the claim made at the Census website or do they appear to agree with it?  EXPLAIN.