**MATH 221 COMPLETE COURSE**

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**MATH 221 COMPLETE COURSE**

**Discussions**

**Week 1**

Descriptive Statistics (graded) |

If you were given a large data set such as the sales over the last year of our top 1,000 customers, what might you be able to do with this data? What might be the benefits of describing the data?

**Week 2**

Regression (graded) |

Suppose you are given data from a survey showing the IQ of each person interviewed and the IQ of his or her mother. That is all the information that you have. Your boss has asked you to put together a report showing the relationship between these two variables. What could you present and why?

**Week 3**

Statistics in the News (graded) |

Keep your eyes and ears open as you read or listen to the news this week. Find/discover an example of statistics in the news to discuss the following statement that represents one of the objectives of statistics analysis: “Statistics helps us make decisions based on data analysis.” Briefly discuss how the news item or article meets this objective. Cite your references.

**Week 4**

Discrete Probability Variables (graded) |

What are examples of variables that follow a binomial probability distribution? What are examples of variables that follow a Poisson distribution? When might you use a geometric probability?

**Week 5**

Interpreting Normal Distributions (graded) |

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

**Week 6**

Confidence Interval Concepts (graded) |

Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula.

**Week 7**

Rejection Region (graded) |

How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?

Statistics – Lab Week 2

Name:_______________________

#### MATH221

Statistical Concepts:

- Using Minitab
- Graphics
- Shapes of Distributions
- Descriptive Statistics
- Empirical Rule

# DATA IN MINITAB

Ø Minitab is a powerful, yet user-friendly, data analysis software package. You can launch Minitab by finding the icon and double clicking on it. After a moment you will see two windows, the Session Window in the top half of the screen and the Worksheet or Data Window in the bottom half.

Ø Data have already been formatted and entered into a Minitab worksheet. Go to the eCollege Doc sharing site to download this data file. The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Minitab Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. Included with this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions.

Ø Complete the questions after the Code Sheet and paste the Graphs from Minitab in the grey areas for question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations. The completed iLab Word Document with your responses to the questions will be the ONE and only document submitted to the dropbox. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2iLab.

Code Sheet

Do NOT answer these questions. The Code Sheet just lists the variables name and the question used by the researchers on the survey instrument that produced the data that are included in the Minitab data file. This is just information. The first question for the lab is after the code sheet.

Variable Name |
## QUESTION |

Drive | Question 1 – How long does it take you to drive to the school on average (to the nearest minute)? |

State | Question 2 – What state/country were you born? |

Temp | Question 3 – What is the temperature outside right now? |

Rank | Question 4 – Rank all of the courses you are currently taking. The class you look most forward to taking will be ranked one, next two, and so on. What is the rank assigned to this class? |

Height | Question 5 – What is your height to the nearest inch? |

Shoe | Question 6 – What is your shoe size? |

Sleep | Question 7 – How many hours did you sleep last night? |

Gender | Question 8 – What is your gender? |

Race | Question 9 – What is your race? |

Car | Question 10 – What color of car do you drive? |

TV | Question 11 – How long (on average) do you spend a day watching TV? |

Money | Question 12 – How much money do you have with you right now? |

Coin | Question 13 – Flip a coin 10 times. How many times did you get tails? |

Die1 | Question 14 – Roll a six-sided die 10 times and record the results. |

Die2 | |

Die3 | |

Die4 | |

Die5 | |

Die6 | |

Die7 | |

Die8 | |

Die9 | |

Die10 |

Creating Graphs

- 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). In this same labels window, select the tab- Slice Labels and click on all; Category name; Frequency; Percent; Draw a line from label to slice and then 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.
- 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. - Create a stem and leaf chart for the variable Money – Pull up
**Graph > 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.**

# CALCULATING DESCRIPTIVE STATISTICS

- 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.

Mean | Standard deviation | |

Females | ||

Males |

Ø Select **File > Save Worksheet As** to save the data set. You must either keep a copy of this data or download it again off the web site for future labs.

Short Answer Writing Assignment

All answers should be complete sentences.

- What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.
- What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.
- What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer.
- 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.
- 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.
- Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.
- Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.

Statistics – Lab Week 4

Name:_______________________

MATH221

Statistical Concepts:

- Probability
- Binomial Probability Distribution

# CALCULATING BINOMIAL PROBABILITIES

**Ø Open a new MINITAB worksheet.**

Ø We 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 to **Probability**. 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 button **OK**and the probabilities will be displayed in the Worksheet.

Ø Now 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.

Ø Finally, 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**

- Create plots for the three binomial distributions above. Select
**Graph > 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.

**Calculating Descriptive Statistics**

Ø Open the class survey results that were entered into the MINITAB worksheet.

- Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up
**Stat > Basic Statistics > Display Descriptive Statistics**and set**Variables:**to the coin. The output will show up in your Session Window. Type the mean and the standard deviation here.

Mean:Standard deviation: |

Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions.

- List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being ½. (Complete sentence not necessary)

P(x=0) | P(x=6) | |||

P(x=1) | P(x=7) | |||

P(x=2) | P(x=8) | |||

P(x=3) | P(x=9) | |||

P(x=4) | P(x=10) | |||

P(x=5) |

- Give the probability for the following based on the MINITAB calculations with the probability of a success being ½. (Complete sentence not necessary)

P(x?1) | P(x<0) | |||

P(x>1) | P(x?4) | |||

P(4 | P(x<4 or x?7) |

- Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ½. Either show work or explain how your answer was calculated. Mean =
*np*, Standard Deviation =

Mean:Standard deviation: |

- Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¼ and compare to the results from question 5. Mean =
*np*, Standard Deviation =

Mean:Standard deviation:Comparison: |

- Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¾ and compare to the results from question 6. Mean =
*np*, Standard Deviation = - Explain why the coin variable from the class survey represents a binomial distribution.

he mean and standard deviation for the coin variable and compare these to the mean and standard deviation for the binomial distribution that was calculated in question 5. Explain how they are related. Mean = *np*, Standard Deviation =

Week 6 ilab

Statistical Concepts:

• Data Simulation

• Discrete Probability Distribution

• Confidence Intervals

Calculations for a set of variables

? Open the class survey results that were entered into the MINITAB worksheet.

? We 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 Statistics and select 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.

? We 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

? Calculate 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

? Open the class survey results that were entered into the MINITAB worksheet.

? We 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 the OK button and the results will appear in your Session Window.

? We are also interested in the same analysis with a 99% confidence interval. Use the same steps except select the Options button and change the Confidence level: to 99.

**MATH 221 FINAL EXAM**

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