# Devry MATH221 All Discussions With Sample Answers

### MATH221 Week 1 Discussion Questions

#### Descriptive Statistics

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?

#### Post-Class Topic: Social Media’s Use of Data

This century is already being characterized as the era of “big data.” You are probably active or at least knowledgeable about the proliferation of various social media outlets, like Facebook, Twitter, LinkedIn and flickr. Do you feel like too much personal data is retained forever? Do you have any concerns about how your personal data is used? Or, are you satisfied that most studies based on personal data collected by large companies maintain sufficient controls and respect an individual’s privacy by only publishing aggregate figures (or “statistics”) which summarize trends? (There is no correct answer, just informed opinions.)

### MATH221 Week 2 Discussion Questions

#### Regression

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?

#### Post-Class Topic: Correlation and Causation

If two variables are strongly correlated, does it necessarily always follow that there is a direct cause-and-effect relationship between the two variables? Can you think of two variables which are often associated with each other and are highly correlated, but there is no direct cause-and-effect relationship between them? For example, do you think it is a correct conclusion that watching soap operas gives girls eating disorders like anorexia if a study showed that “girls who watch soap operas are more likely to have eating disorders.”

### MATH221 Week 3 Discussion Questions

#### Statistics in the News

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.

### MATH221 Week 4 Discussion Questions

#### Discrete Probability Variables

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?

#### Post-Class Topic: Interpreting the “Most Likely” outcome of a Binomial

Do you think that the “most likely” outcome in a binomial distribution is the outcome that will occur most of the time?” For example, what is the “most likely” composition of a four-member committee chosen randomly from a large population that is 50% women and 50% men? What is the probability of the committee composed by two mean and two women? What is the probability of the committee containing one man and three women? What is the probability of the committee containing three men and one woman?

### MATH221 Week 5 Discussion Questions

#### Interpreting Normal Distributions

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?

#### Post-Class Topic: Central Limit Theorem

Explain what property associated with the Central Limit Theorem you consider the most important contribution, enabling the use of the normal distribution for sample means with large sample size.

### MATH221 Week 6 Discussion Questions

#### Confidence Interval Concepts

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.

### Post-Class Topic: Confidence Intervals and Hypothesis Testing (graded)

The EPA will grant a tax credit if the city-highway mileage estimate is at least 31 mpg.Construct the 95% and 99% confidence intervals for the mean mpg [miles per gallon] if we have a data sample with 49 observations of mileage of a new car model, with x-bar = 31.5531 mpg and known std. dev. sigma = 0.8 mpg. Which CI is wider and why? Would the EPA grant a tax credit if the 99% CI is (31.26, 31.85) and why? This is an example of hypothesis testing using CIs. If the EPA minimum qualifying mileage were 33 mpg, instead of 31 mpg, would the EPA grant a tax credit with the same 99% CI?

### MATH221 Week 7 Discussion Questions

#### Rejection Region

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?