WHICH STATISTIC(S) WILL YOU USE TO DESCRIBE THE SPREAD OF THE DISTRIBUTION?

02 May WHICH STATISTIC(S) WILL YOU USE TO DESCRIBE THE SPREAD OF THE DISTRIBUTION?

MATH 1530 CAPSTONE TECHNOLOGY PROJECT SUMMER 2015Problem 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 variables 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 AGEinto 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 ofall 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 2014survey 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 students age to predict daily handwashes.

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.

Problem 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 GENDERQuestion 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 column12 ‘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 dont want to display information for students that didnt 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_PENALTYQuestion 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 dont want to display information for students that didnt 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.

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