**MATH399 Week 1 Discussion Latest 2018 January**

WEEK 1: DESCRIPTIVE STATISTICS

3232 unread replies.5252 replies.

If you were given a large data set (i.e., sales over the last year of our top 100 customers), what might you be able to do with these data? What might be the benefits of describing the data?

**MATH399 Week 2 Discussion Latest 2018 January**

WEEK 2: REGRESSION

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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?

**MATH399 Week 3 Discussion Latest 2018 January**

WEEK 3: PROBABILITY AND ODDS

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The odds of winning a game are given as 1:25. What is the probability that you will win this game? What is the probability that you will lose this game? In your follow-up replies, consider which number in the odds ratio needs to change and how it needs to change in order to increase the probability of winning. (Note: See page 145 in the text for a discussion on odds.)

**MATH399 Week 4 Discussion Latest 2018 January**

WEEK 4: DISCRETE PROBABILITY VARIABLES

4040 unread replies.9595 replies.

Provide an example that follows either the binomial or Poisson distribution, and explain why that example follows that particular distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then, show the work (or describe the technology steps), and solve that probability example.

**MATH399 Week 5 Discussion Latest 2018 January**

WEEK 5: INTERPRETING NORMAL DISTRIBUTIONS

8383 unread replies.9090 replies.

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?

**MATH399 Week 6 Discussion Latest 2018 January**

WEEK 6: CONFIDENCE INTERVAL CONCEPTS

2727 unread replies.3232 replies.

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.

**MATH399 Week 7 Discussion Latest 2018 January**

WEEK 7: REJECTION REGION

7575 unread replies.9696 replies.

How is the rejection region defined, and how is that related to 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?

**MATH399 Week 2 Lab Latest 2018 January**

MATH399 Statistics—Lab Week 2

Question 1 is worth 5 points and each question after that is worth 4.5 points, for a total of 50 points for the lab.

Name:_______________________

Statistical Concepts:

· Using Excel

· Graphics

· Shapes of distributions

· Descriptive statistics

NOTE: Directions for all labs are given based on Excel 2013 for Windows. If you have another version of Excel, you may need to research how to do the same steps.

# Data in Excel

Ø Excel is a powerful, yet user-friendly, data analysis software package. You can launch Excel by finding the icon and double clicking on it*. There are detailed instructions on how to obtain the graphs and statistics you need for this lab in each question. There is also a link to an Excel how to document on the iLab page where you opened this file. Further, if you need more explanation of the Excel functions you can do an internet search on the function like “Excel standard deviation” or “Excel pivot table” for a variety of directions and video demonstrations.*

Ø Data have already been formatted and entered into an Excel worksheet. You will see the link on the page with this lab document.The names of each variable from the survey are in the first row of the worksheet. All other rows of the worksheet represent certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. Below, you will find a code sheet that identifies the correspondence between the variable names and the survey questions.

__SurveyCode 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 Excel 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: In what state/country were you born? |

Shoe | Question 3: What is your shoe size? |

Height | Question 4: What is your height to the nearest inch? |

Sleep | Question 5: How many hours did you sleep last night? |

Gender | Question 6: What is your gender? |

Car | Question 7: What color of car do you drive? |

TV | Question 8: How long (on average) do you spend a day watching TV? |

Money | Question 9: How much money do you have with you right now? |

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

__Frequency Distributions__

1. Create a frequency table for the variable State.In the Excel file, you can click on*Data* and then*Sort* and choose*State* as the variable on which to sort. Once sorted, you can count how many students are from each state. From that table, use a calculator to determine the relative percentages, as well as the cumulative percentages.

In the box below, type the states from the database in a column to the left, then type the counts, and relative and cumulative frequencies to the right of the respective state. Using the data in the table, make a statement about what the frequency counts or percentages tell about the data.

__Creating Graphs__

2. Create a bar chart for the frequency table in Question 1. Select the State variable values. Click on*Insert*and then click on the arrow on the bottom right of the*Charts* area and select*Clustered Column*and click*OK*. (Again, different versions of Excel may need different directions.) Add an appropriate title and axis label.*Copy and paste the graph here.*

3. Create a pie chart for the variable Car. Select the column with the Car variable, including the title of Car. Click on*Insert*, and then*Recommended Charts*. It should show a clustered column and click*OK*. Once the chart is shown, right click on the chart (main area)and select*Change Chart Type*. Select*Pie* and*OK*. Click on the pie slices, right click*Add Data Labels*, and select*Add Data Callouts*. Add an appropriate title.Copy and paste the chart here.

4. Create a histogram for the variable Height. Use the strategies in the text to create a frequency table of the heights using the categories of 60–64, 65–69, 70–74, and 75–79. It may be helpful to sort the data based on the Height variable first. Create a new worksheet in Excel by clicking on the + along the bottom of the screen and type in the categories and the frequency for each category. Then, select the frequency table, click on*Insert*, then*Recommended Charts* and choose the column chart shown and click*OK*. Right-click on one of the bars and select*Format Data Series*. In the pop up box, change the*Gap Width* to 0. Add an appropriate title and axis label.Copy and paste the graph here.

5. Create a stem and leaf chart for the variable Money, using only the whole dollar amounts. This must be done by hand, as Excel cannot do this type of chart. Using the tens value as the stem and the ones value for the leaves, type a stem and leaf plot into the box below. It may be helpful to sort the data based on the Money variable first.

# Calculating Descriptive Statistics

6. Calculate descriptive statistics for the variable Height by Gender. Click on*Insert* and then*Pivot Table*. Click in the top box and select all the data (including labels) from Height through Gender. Also click on new worksheet and then*OK*. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the*Rows* box and Height is in the*Values* box. Click on the down arrow next to Heigh**t** in the Values box and select*Value Field Settings*. In the pop up box, click*Average*,then*OK*. Type in the averages below. Then, click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on*StdDev*thenOK. Type the standard deviations below.

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 website for future labs.

__Short Answer Writing Assignment__

All answers should be complete sentences.

7. What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.

8. What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.

9. What is seen in the stem and leaf plot for the money variable (including the shape)? Explain your answer.

10. 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.

11. 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.

**MATH399 Week 4 Lab Latest 2018 January**

MATH399 Statistics

Week 4 Lab

Name: _______________________

Statistical Concepts:

· Probability

· Binomial Probability Distribution

Calculating Binomial Probabilities

Ø Open a new Excelworksheet.

1. Open spreadsheet

2. In cell A1 type “success” as the label

3. Under that in column A, type 0 through 10 (these will be in rows 2 through 12)

4. In cell B1, type “one fourth”

5. In cell B2, type “=BINOM.DIST(A2,10,0.25,FALSE)” [NOTE: if you have Excel 2007, then the formula is BINOMDIST without the period]

6. Then copy and paste this formula in cells B3 through B12

7. In cell C1, type “one half”

8. In cell C2, type “=BINOM.DIST(A2,10,0.5,FALSE)”

9. Copy and paste this formula in cells C3 through C12

10. In cell D1 type “three fourths”

11. In cell D2, type “=BINOM.DIST(A2,10,0.75,FALSE)”

12. Copy and paste this formula in cells D3 through D12

__Plotting the Binomial Probabilities__

1. Create plots for the three binomial distributions above. You can create the scatter plots in Excel by selecting the data you want plotted, clicking on INSERT, CHARTS, SCATTER, then selecting the first chart shown which is dots with no connecting lines.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 in the grey area below. (12 points)

__Calculating Descriptive Statistics__

Ø You will use the same class survey results that were entered into the Excel worksheet for the Week 2 iLab Assignment for question 2.

2. Calculate descriptive statistics for the variable(Coin) where each of the students flipped a coin 10 times. Round your answers to three decimal places and typethe mean and the standard deviation in the grey area below. (4 points)

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. Round all numeric answers to three decimal places.__

3. List the probability value for each possibility in the binomial experiment __calculated at the beginning of this lab__, which was calculated with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places) (10 points)

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) |

4. Give the probability for the following based on the calculations __in question 3 above__, with the probability of a success being ½.(Complete sentence not necessary; round your answers to three decimal places) (12 points)

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

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

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

5. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½and n = 10. Either show work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = *np*, Standard Deviation = (4 points)

Mean =np:
Standard Deviation = : |

6. Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment. (4 points)

7. Compare the mean and standard deviation for the Coin variable (question 2) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences. (4 points)

Mean from question #2:
Standard deviation from question #2: Mean from question #5: Standard deviation from question #5: Comparison and explanation: |

**MATH399 Week 6 Lab Latest 2018 January**

MATH 399N Statistics for Decision Making

Week 6 iLab

Statistical Concepts:

· Data Simulation

· Confidence Intervals

· Normal Probabilities

__Short Answer Writing Assignment__

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and then find the maximum error. Then we can use a calculator to find the interval, (x – E, x + E).

First, find the mean. Under that column, in cell E37, type **=AVERAGE(E2:E36)**. Under that in cell E38, type **=STDEV(E2:E36)**. Now we can find the maximum error of the confidence interval. To find the maximum error, we use the “confidence” formula. In cell E39, type **=CONFIDENCE.NORM(0.05,E38,35)**. The 0.05 is based on the confidence level of 95%, the E38 is the standard deviation, and 35 is the number in our sample. You then need to calculate the confidence interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x+E).

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. (5 points)

Then, you can go down to cell E40 and type **=CONFIDENCE.NORM(0.01,E38,35)** to find the maximum error for a 99% confidence interval. Again, you would need to use a calculator to subtract this and add this to the mean to find the actual confidence interval.

2. Give and interpret the 99% confidence interval for the hours of sleep a student gets. (5 points)

3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs. (10 points)

4. Find the mean and standard deviation of the DRIVE variable by using **=AVERAGE(A2:A36)** and **=STDEV(A2:A36)**. Assuming that this variable is normally distributed, what percentage of data would you predict would be less than 40 miles? This would be based on the calculated probability. Use the formula **=NORM.DIST(40, mean, stdev,TRUE)**. Now determine the percentage of data points in the dataset that fall within this range. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction? (15 points)

Mean ______________ Standard deviation ____________________
Predicted percentage ______________________________ Actual percentage _____________________________ Comparison ___________________________________________________ ______________________________________________________________ |

5. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Subtract the probabilities found through **=NORM.DIST(70, mean, stdev, TRUE)** and **=NORM.DIST(40, mean, stdev, TRUE)** for the “between” probability. To get the probability of over 70, use the same **=NORM.DIST(70, mean, stdev, TRUE)** and then subtract the result from 1 to get “more than”. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference? (15 points)

Predicted percentage between 40 and 70 ______________________________
Actual percentage _____________________________________________ Predicted percentage more than 70 miles ________________________________ Actual percentage ___________________________________________ Comparison ____________________________________________________ _______________________________________________________________ Why? __________________________________________________________ ________________________________________________________________ |