COMPLETE COURSE MATH221 COMPLETE COURSE ## MATH 221 Week 1 DQ Descriptive Statistics

1.Determine whether the given value is a statistic or a parameter.
A sample of students is selected and it is found that 35% own a computer
Study plan 1.1.41

2.Determine whether the underlined numerical value is a parameter or statistic. Explain your reasoning.
A certain zoo found that 8% of its 843 animals were nocturnal
Study Plan: 1.1.37
3.Suppose a survey of 568 women in the United States found that more than 56% are the primary investor in their household. Which part of the survey represents the descriptive statistics? Make an inference based on the results of the survey.
4.How is a sample related to a population?
5.Determine whether the variable is qualitative or quantitative
a.Goals scored in a hockey game
b.Favorite musical instrument
Study plan 1.2.7
6.What is an inherent Zero? Describe an example that has an inherent zero.
Study plan 1.2.31
7.Which method of data collection should be used to collect data for the following study.
A study of the health of 164 kidney transplant patients at a hospital.
Study plan 1.3.11
8.Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits and the upper class limits.
Minimum = 13, maximum = 84, 6 classes
Study plan 2.1.11
9.Some graph questions to study: Study Plan 2.1.19, 2.1.26, 2.1.27
10.Students in an experimental psychology class did research on depression as sign of stress. A test was administered to a sample of 30 students. The scores are shown below.
43 50 10 90 77 35 64 36 42 72
54 62 35 75 50 72 36 29 39 61
48 63 35 41 21 36 50 46 86 14
a. Find the 10% trimmed mean of the data.
b. Find Mean
c. Find Median
D. Find Mode
E. Midrange
Please use the paste to clipboard from the data set to work in excel or in minitab
Study plan 2.3.65
11.Find the range, mean, variance and standard deviation of the sample data set.
7 10 17 15 5 11 16 6 13
Study plan 2.4.13

## MATH 221 Week 2 DQ Regression

1. Construct a scatter plot and determine the type of correlation using r for the following data
The ages(in years) of 6 children and the number of words in their vocabulary
 Age, x 1 2 3 4 5 6 Vocabulary size,y 250 950 1200 1450 1800 2650
a) Display the data in a scatter plot
b) Calculate the correlation coefficient r
c) Make a conclusion about the type of correlation
Study plan 9.1.22, 9.1.24
2. Suppose the scatter plot shows the results of a survey of 42 randomly selected males ages 24 to 35. Using age as the explanatory variable, choose the appropriate description for the graph, Explain your reasoning.
a) Age and body temperature
b) Age and balance on student loans
c) Age and income
d) Age and height

PLEASE SEE THE DOCUMENT ATTACHED FOR THIS GRAPH
The response variable is ____________ because you would expect this variable and age to have _________________ and ____________variation for adult males.
Study plan 9.2.17
3. 3. Identify the explanatory and the response variable.
A farmer wants to determine if the temperature received by similar crops can be used to predict the harvest of the crop.
The explanatory variable is _________
The response variable is ____________

## MATH 221 Week 2 Ilab Correlation and Regression

1.Create a Pie Chart for the variable Car – Pull up Graph > Pie Chart and click in the categories variables box so that the list of variables will show up on the left. Now double click on the variable name ‘Car” in the box at the left of the window. Include a title by clicking on the “Labels…” button and typing it in the correct text area (put your name in as the title) and click OK. Click OK again to create graph. Click on the graph and use Ctrl+C to copy and come back here, click below this question and use Ctrl+V to paste it in this Word document.
2.Create a histogram for the variable Height – Pull up Graph > Histograms and choose “Simple”. Then set the graph variable to “height”. Include a title by clicking on the “Labels…” button and typing it in the correct text area (put your name in as the title) and click OK. Copy and paste the graph here.
3. Create a stem and leaf chart for the variable Money – Pull upGraph> Stem-and Leaf and set Variables: to “Money”. Enter 10 for the Increment: and click OK.
The leaves of the stem-leaf plot will be the one’s digits of the values in the “Money” variable. Note: the first column of the stem-leaf plot that you create is the count. The row with the count in parentheses includes the median. The counts below the median cumulate from the bottom of the plot.Copy and paste the graph here.
4.Calculate descriptive statistics for the variable Height by Gender – Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to Height. Check By variable: and enter Gender into this text box. Click OK. Type the mean and the standard deviation for both males and females in the space below this question.
5.What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.
6.What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.
7. What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer.
8. Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers.
9.Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.
10.Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.
11.Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.

## MATH 221 Week 3 DQ Statistics in the News

PROBABILITY DISTRIBUTIONS
Objective - CONCEPTS:
1. Determine which of the following numbers could not represent the probability of an event
0, 0.008, -0.6, 65%, 715/1206, 60/47
Study plan: 3.1.1, 3.1.2, 3.1.7, 3.1.8

Objective-Sample Space
2. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
Determining a person’s grade Freshman (F), Sophomore (So), Junior (J), Senior (Se) and gender (male(M) Female (F))
Study Plan: 3.1.15, 3.1.17, 3.1.19

Objective-Simple Events
3. Determine the number of outcomes in the event. Decide whether the event is a simple event or not.
You randomly select one card from a standard deck. Event A is selecting a red four.
Study Plan: 3.1.21, 3.1.23

Objective-Frequency Distribution

4. Use the frequency distribution below, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range.
Not between 25 and 34 years old
 Ages of voters Frequency 18 to 20 7.4 21 to 24 11.5 25 to 34 21.8 35 to 44 25.5 45 to 64 56.8 65 and over 28.7
Study Plan: 3.1.55, 3.1.57, 3.1.59, 3.1.61, 3.1.63
Objective-Distinguish between independent and dependent events
5. Researchers found that people with depression are four times more likely to have a breathing-related sleep disorder that people who are not depressed. Identify the two events described in the study. Do the results indicate that the events are independent or dependent?
Study Plan: 3.2.7, 3.2.11, 3.2.13, 3.2.15
Objective-Conditional Probability
6. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Seven out of 10 women with this mutation develop breast cancer.
a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.
b. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.
c. Are the events of carrying this mutation and developing breast cancer independent or dependent events.
Study Plan: 3.2.17, 3.2.27
Objective-Multiplication Rule to Find Probabilities
7. A study found that 38% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-two percent of the ART pregnancies resulted in multiple births.
a. Find the probability that a randomly selected ART cycle resulted in a pregnancy and produced a multiple birth.
b. Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.
c. Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? Explain
Study Plan: 3.2.21, 3.2.23, 3.2.26
Objective-Mutually exclusive
8. Decide if the events are mutually exclusive.
Event A: Randomly selecting someone treated with a certain medication.
Event B: Randomly selecting someone who received no medication
Study Plan: 3.3.7, 3.3.9, 3.3.11
9. During a 52-Week period, a company paid overtime wages for 16 Weeks and hired temporary help for 8 Weeks. During 4 Weeks, the company paid overtime and hired temporary help.
a. Are the events “Selecting a Week that contained overtime wages” and “selecting a Week that contained temporary help wages” mutually exclusive
b. If an auditor randomly examined the payroll records for only one Week, what is the probability that the payroll for that Week contained Overtime wages or temporary help wages?
Study Plan: 3.3.13, 3.3.15, 3.3.17,3.3.25
Objective-Permutation and Combination
10. Find 37 C2
Study Plan: 3.4.8, 3.4.11, 3.4.13, 3.4.14
Objective-Counting Principles
11. A certain lottery has 30 numbers. In how many different ways can 5 of the numbers be selected? Assume that order of selection is not important
Study Plan: 3.4.21, 3.4.22, 3.4.23, 3.4.25
Objective-CONSTRUCT PROBABILTIES
12. A frequency distribution is shown below.
The number of dogs per household in a small town
Dogs 0 1 2 3 4 5
Households 1128 424 167 48 27 17
a. Use the frequency distribution to construct a probability distribution
 x P(x) 0 1 2 3 4 5
b. Find the mean of the probability distribution
c. Find the variance of the probability distribution
d. Find the standard deviation of the probability distribution
Study Plan: 4.1.13, 4.1.15, 4.1.17, 4.1.19, 4.1.21, 4.1.23, 4.1.25, 4.1.27, 4.1.29, 4.1.31, 4.1.35, 4.1.37, 4.1.39

## MATH 221 Week 4 DQ Discrete Probability Variables

1. About 40% of babies born with a certain ailment recover fully. A hospital is caring for seven babies with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment? If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.
STUDY PLAN: 4.2.9, 4.2.11

OBJECTIVE: Find the MEAN, VARIANCE AND STANDARD DEVIATION OF THE binomial distribution
2. Find the mean, variance and standard deviation of the binomial distribution n= 123, p= 0.69
STUDY PLAN: 4.2.15
OBJECTIVE: FIND BINOMIAL PROBABILITIES USING TECHNOLOGY
3. 47% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is
a. Exactly eight
b. At least eight
c. Less than eight
STUDY PLAN: 4.2.19, 4.2.21, 4.2.23, 4.2.25
OBJECTIVE: FIND PROBABILITIES FOR POISSON DISTRIBUTION USING technology 4. Given that x has a Poisson distribution with mean mu= 4, what is the probability that x= 6?
STUDY PLAN: 4.3.5

# Calculating Binomial Probabilities

ØOpen a new MINITAB worksheet.
ØWe are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc> Probability Distributions > Binomial and select the radio button that corresponds toProbability. Enter 10 for the Number of trials: and enter 0.25 for the Event probability:. For the Input column: select ‘success’ and for the Optional storage: select ‘one fourth’. Click the buttonOK and the probabilities will be displayed in the Worksheet.
ØNow we will change the probability of a success to ½. In column C3 enter the words ‘one half’ as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5.
ØFinally, we will change the probability of a success to ¾. In column C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.75.
Plotting the Binomial Probabilities
1.Create plots for the three binomial distributions above. SelectGraph> Scatter Plot and Simple then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on the variable name and using the “select” button below the list of variables. Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’. Paste those three scatter plots below.

## MATH 221 Week 5 DQ Interpreting Normal Distributions

OBJECTIVE: CONCEPTS

1.What requirements are necessary for a normal probability distribution to be a standard normal distribution?
STUDY PLAN: 5.1.2, 5.1.3, 5.1.7

OBJECTIVE: COMPUTE AND INTERPRET Z-SCORES of NORMAL DISTRIBUTIONS

2.The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 122, 113, 106 and 128 millimeters of mercury. The graph of the standard normal distributions is shown below. Complete a) and b) PLEASE SEE ATTACHED DOCUMENT FOR GRAPHS
a.Without converting to z scores, match the values with the letters A, B, C, and D on the given graph of the standard normal distribution.
b.Find the z-score that corresponds to each value and check your answers to part (a) (Round to two decimals as needed)
STUDY PLAN: 5.1.41, 5.1.43

OBJECTIVE: FIND PROBABILITIES USING THE STANDARD NORMAL DISTRIBUTION

3.For the standard normal distribution shown below, find the probability of z occurring in the indicated on the graph. Please see attached document
STUDY PLAN: 5.1.45, 5.1.47, 5.1.55, 5.1.57
OBJECTIVE: FIND PROBABILITIES FOR NORMALLY DISTRIBUTED VARIABLES

4.Assume the random variable x is normally distributed with mean mu= 50 and
standard deviation sigma= 7. Find P(x > 42)
STUDY PLAN: 5.2.1, 5.2.3, 5.2.5, 5.2.7, 5.2.9, 5.2.11, 5.2.15
OBJECTIVE: APPLICATIONS OF NORMAL DISTRIBUTION

5.Use the normal distribution of SAT writing scores with mean = 493 and standard deviation = 111.
a. What percentage of SAT writing scores are less than 600?
b. If 1000 SAT writing scores are randomly selected, about how many would you expect to be greater than 550?
STUDY PLAN: 5.2.21, 5.2.23, 5.2.25, 5.2.27
OBJECTIVE: FIND A Z SCORE GIVEN THE AREA UNDER THE NORMAL CURVE
6.Find the z score that corresponds to the cumulative area of 0.049

STUDY PLAN: 5.3.1, 5.3.3, 5.3.5, 5.3.7, 5.3.17, 5.3.19, 5.3.21, 5.3.23, 5.3.25, 5.3.27, 5.3.29
OBJECTIVE: APPLICATION OF NORMAL DISTRIBUTION

7.In a survey of women in a certain country (ages 20- 29), the mean height was 65.3 inches with a standard deviation of 2.67 inches.
a.What height represents the 98th percentile?
b.What height represents the first quartile?
STUDY PLAN: 5.3.31, 5.3.33, 5.3.35, 5.3.38, 5.3.39, 5.3.41
OBJECTIVE: Interpret sampling distributions

8.A population has a mean mu= 86 and a standard deviation sigma =20. Find the mean and standard deviation of a sampling distribution of sample means with a sample size n= 268
STUDY PLAN: 5.4.1, 5.4.3
OBJECTIVE: CENTRAL LIMIT THEOREM

9.Use the central limit theorem to find the mean and standard error of the mean of the sampling distribution.
The mean price of photo printers on a website is \$221 with a standard deviation of \$69. Random samples of size 34 are drawn from the population and the mean of each sample is determined. (ROUND ANSWERS TO THREE DECIMALS)
10.The population mean annual salary for environmental compliance specialists is about \$61,500. A random sample of 34 specialists is drawn from this population. What is the probability that the mean salary is less than \$59,000? Assume standard deviation sigma= \$5800?

## MATH 221 Week 6 DQ Confidence Interval Concepts

1. Find the margin of error for the given values of c = 0.95 , s= 3.6 and n= 36
(Round to three decimal places as needed)
STUDY PLAN: 6.1.13, 6.1.15
OBJECTIVE: CONSTRUCT AND INTERPRET CONFIDENCE INTERVALS FOR THE POPULATION MEAN
2. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.
A random sample of 37 gas grills has a mean price of \$637.70 and a standard deviation of \$58.30
(Round to one decimal place as needed)
STUDY PLAN: 6.1.35, 6.1.36, 6.1.37, 6.1.40
OBJECTIVE: DETERMINE THE MINIMUM SAMPLE SIZE
3. A doctor wants to estimate the HDL cholesterol of all 20- to 29- year-old females. How many subjects are needed to estimate the HDL cholesterol within 4 points with 99% confidence assuming standard deviation sigma = 19.4? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required?
(Round to the next whole number)
STUDY PLAN: 6.1.53, 6.1.56
OBJECTIVE: FIND A CRITICAL VALUE
4. Find the critical value tc for the confidence level c= 0.80 and sample size n= 17
(Round to the nearest thousandth as needed)
STUDY PLAN: 6.2.1, 6.2.3
OBJECTIVE: CONSTRUCT AND INTERPRET CONFIDENCE INTERVALS FOR THE POPULATION MEAN
5. The monthly incomes for 12 randomly selected people, each with a bachelor’s degree in economics, are shown below.
4450.05 4596.56 4366.72 4455.33 4151.74 3727.63
4283.45 4527.71 4407.26 3946.96 4023.09 4221.67
a. Find the sample mean. (Round to one decimal place as needed)
b. Find the sample standard deviation (Round to one decimal place as needed)
c. Construct the 99% confidence interval for the population mean mu.
STUDY PLAN: 6.2.5, 6.2.7, 6.2.24, 6.3.11, 6.3.13
OBJECTIVE: DETERMINE THE MINIMUM SAMPLE SIZE
6. A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed Internet access. Her estimate must be accurate within 2% of the true proportion.
a. Find the minimum sample size needed, using a prior study that found that 52% of the respondents said they have high-speed Internet access.
(Round to the nearest whole number as needed)
b. What is the minimum sample size needed assuming that no preliminary estimate is available?
STUDY PLAN: 6.3.17, 6.3.18

## MATH 221 Week 6 ilab Confidence Intervals

Statistical Concepts:
·Data Simulation
·Discrete Probability Distribution
·Confidence Intervals

# Calculations for a set of variables

ØOpen the class survey results that were entered into the MINITAB worksheet.
ØWe want to calculate the mean for the 10 rolls of the die for each student in the class. Label the column next to die10 in the Worksheet with the word mean. Pull up Calc> Row Statisticsandselect the radio-button corresponding to Mean. For Input variables: enter all 10 rows of the die data. Go to the Store result in: and select the mean column. Click OK and the mean for each observation will show up in the Worksheet.
ØWe also want to calculate the median for the 10 rolls of the die.Label the next column in the Worksheet with the word median. Repeat the above steps but select the radio-button that corresponds to Median and in the Store results in: text area, place the median column.

# Calculating Descriptive Statistics

ØCalculate descriptive statistics for the mean and median columns that where created above. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to mean and median. The output will show up in your Session Window. Print this information.

# Calculating Confidence Intervals for one Variable

ØOpen the class survey results that were entered into the MINITAB worksheet.
ØWe are interested in calculating a 95% confidence interval for the hours of sleep a student gets. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to Sleep. Click theOK button and the results will appear in your Session Window.
ØWe are also interested in the same analysis with a 99% confidence interval. Use the same steps except select theOptions button and change the Confidence level: to 99.

## MATH 221 Week 7 DQ Rejection Region

1. A study claims that the mean survival time for certain cancer patients treated immediately with chemotherapy and radiation is 16 months.
STUDY PLAN: 7.1.29, 7.1.30

OBJECTIVE: TEST A CLAIM ABOUT A MEAN USING CRITICAL VALUES
2. A company that makes colas drinks states that the mean caffeine content per 12-ounce bottle of cola is 45 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 43.3 milligrams with a standard deviation of 6.8 milligrams. At alpha = 0.05, can you reject the company’s claim?
STUDY PLAN: 7.2.35, 7.2.37

OBJECTIVE: TEST A CLAIM ABOUT A MEAN USING T- TEST
3. Use technology and a t-test to test the claim about the population mean at the given level of significance aloha using the given sample statistics. Assume the population is normally distributes. Claim mu > 71; alpha = 0.01; sample mean = 73.1, s= 3.6 , n= 27
STUDY PLAN 7.3.23, 7.3.31

OBJECTIVE: Find P Value for t- test
4. For your study on the food consumption habits of teenage males, you randomly select 10 teenage males and ask each how many 12-ounce servings of soda he drinks each day. The results are listed below. At alpha =0.05, is there enough evidence to support the claim that teenage males drink fewer than three 12-ounce servings of soda per day? Assume the population is normally distributed.
3.9 2.7 2.8 2.6 1.9 3.8 2.6 3.8 3.5 1.1
STUDY PLAN: 7.3.29, 7.3.30

OBJECTIVE: TEST THE CLAIM FOR PROPORTIONS USING REJECTION REGION
5. A humane society claims that less than 35% of U.S households owns a dog. In a random sample of 409 U.S households, 154 say they own a dog. At alpha =0.10, is there enough evidence to support the society’s claim?
STUDY PLAN: 7.4.15, 7.4.17

## MATH 221 All 7 Weeks Discussion Questions

MATH 221 Week 1 DQ Descriptive Statistics
MATH 221 Week 2 DQ Regression
MATH 221 Week 3 DQ Statistics in the News
MATH 221 Week 4 DQ Discrete Probability Variables
MATH 221 Week 5 DQ Interpreting Normal Distributions
MATH 221 Week 6 DQ Confidence Interval Concepts
MATH 221 Week 7 DQ Rejection Region

# MATH 221 Week 8 Final Exam / Devry University

## MATH 221 Entire Course + Final Exam ( 2 sets )

MATH 221 Week 1 DQ Descriptive Statistics
MATH 221 Week 2 DQ Regression
MATH 221 Week 2 IlabCorrelation and Regression
MATH 221 Week 3 DQ Statistics in the News
MATH 221 Week 4 DQ Discrete Probability Variables
MATH 221 Week 4 ilab Discrete Data Probability Distributions
MATH 221 Week 5 DQ Interpreting Normal Distributions
MATH 221 Week 6 DQ Confidence Interval Concepts
MATH 221 Week 6 ilab Confidence Intervals.docx
MATH 221 Week 7 DQ Rejection Region
MATH 221 Week 8 Final Exam1.docx
MATH 221 Week 8 Final Exam2.docx