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**BA 215/ BA215 FINAL EXAM**

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1.Experts have estimated that 25% of all homeless people in the U.S. are veterans. The proportion of Americans in general who are homeless is 0.11. For random samples of 100 people, which is more normal?

2.Many biologists and anthropologists claim that 10 percent of all children conceived in the context of a marriage have been fathered by someone from outside the couple. In this situation, the standard deviation for samples of 225 births is 0.02. If the sample size were decreased, the standard deviation would be

3.The shape of the distribution of sample proportion is approximately normal. If the sample size were decreased to 22, the shape would be

4.The probability of birth by Caesarean in the U.S. is 0.30.If the probability of Caesarean birth is 0.30, and 140 in a sample of 500 births are Caesarean, which of these numbers is X?

5.The probability of being a smoker for a population of college students is 0.20.The standard deviation for samples of 1600 students is 0.01. The standard deviation would be smallest for which of these sample sizes?

6.The shape of the distribution of sample proportion is approximately normal. The shape would be least normal for which of these sample sizes?

7.Suppose 300 in a sample of 1600 students smoke, whereas the population proportion smoking is 0.20. What notation do we use for the number

8.The standard deviation for samples of 1600 students is 0.01. The standard deviation would be smallest for which of these sample sizes?

9.This graph shows the distribution of ACT scores for a population of students. Which of these is your best guess for the probability of a score being greater than 30?

10.Lengths of newborn babies (in inches) have a mean of 20 and a standard deviation of 2. Once z-scores are found, this sketch of the tails of the normal curve can be used to estimate probabilities.

11.Pre-pregnancy BMI for a population of women is approximately normal with a mean of 24 and a standard deviation of 4. Use the sketch of the tails of the z curve to estimate the probability of a BMI below 17:

Use the sketch of the tails of the z curve to estimate the probability of a BMI below 17:

12.Probabilities of scores on a 10-point quiz for a group of students are shown below.

13.Lifespans of male mice have a mean of 860 days and a standard deviation of 40 days. The shape of the distribution is moderately skewed to the left.If we take a sample of mice from this population, how do we denote the mean of their lifespans

14.In 1999, salaries of physician’s assistants in the U.S. had a mean of 68.0 thousand and a standard deviation of 17.0 thousand. The shape of the distribution may have some skewness.In this problem, the number 17 is:

15.Year-level for a population of undergraduate introductory statistics students had probability distribution shown below, the mean level was 1.8 and the standard deviation was 1.0.

16.The proportion of Americans over the age of five who speak another language besides English at home is 0.20. Suppose we take a random sample of 64 Americans over the age of five.Which one of these do we check in order to justify our claim for the mean of the distribution of sample proportion?

17.Online interviews of 1500 parents with children under the age of eight found the proportion who read to their children at least twenty minutes daily to be 0.78. Suppose a reporter would like to claim that more than three-fourths (0.75) of all parents with children under eight read to them at least twenty minutes daily.What notation do we use for the number 0.75?

18.Based on the data provided, can the reporter conclude that more than 0.75 of all parents with children under eight read to them at least twenty minutes daily?

19.The national rate of binge drinking among eighth graders is assumed to be 0.10. We would like to see if the rate of binge drinking among eighth graders in a particular state differs significantly from the national rate. In a survey of 4000 eighth graders from that state, the proportion who reported binge drinking in the previous month was 0.07.The size of the z-statistic is

20.A Type I Error is rejecting the null hypothesis, even though it is true, a Type II Error is failing to reject the null hypothesis, even though it is false.

21.Recently a sample of 250 taxicab drivers in Massachusetts were observed, 17 of them were using seatbelts.How could we obtain a narrower interval?

22.Which of the following would invalidate our confidence interval and subsequent conclusions?

23.In a 2006 poll of 1000 Americans, the proportion who were satisfied with the way things were going in the U.S. was only 0.27.Which of these is denoted by X in this situation?

24.Each student in a class of 80 rolls 8 dice in order to perform inference about the mean of all dice rolls (which happens to be 3.5).Suppose each student uses his or her sample to test the true null hypothesis that the population mean is 3.5 against the two-sided alternative. About how many of these 80 tests should reject at the α = 0.05 level?

25.Suppose that 6 minutes had been the sample standard deviation. Use the fact that the t multiplier for 35 degrees of freedom and 95% confidence is 2.03 to consider a confidence interval for the population mean REM sleep time. Compared to the z interval, the t interval would be

26.For this problem, we will assume that the null hypothesis should be rejected as long as the P-value is less than 0.01. (Note that the area under the t curve for 8 degrees of freedom to the left of -2.896 is 0.01.) Suppose the mean and standard deviation for number of credits taken in a semester by a sample of undergrads are used to test whether the mean credits taken by all undergrads is less than 15. Choose the correct approach under each of the following circumstances. The mean and standard deviation are obtained from a representative sample of 9 undergrads, the data set has a normal appearance.

27.For this problem, we will assume that the null hypothesis should be rejected as long as the P-value is less than 0.01. Suppose the mean and standard deviation for number of credits taken in a semester by a sample of undergrads are used to test whether the mean credits taken by all undergrads is less than 15. Choose the correct conclusion under each of the following circumstances: [You may refer either to the sketch of the t distribution for 8 degrees of freedom, or to the standard normal (z) curve.]28.Based on first and second midterm exam scores for a sample of students, a test is carried out to see if in general students tend to do worse on the second midterm exam.

29.For a sample of 20 students, a test compared their first and second midterm exam scores.

30.An experiment compared reaction times in a driving simulation for a control group (who listened passively to an audio book) with a treatment group (who were obliged to converse using a hands-free cell phone). Software produced the following output.

31.If we test to see if overall reaction times were longer for the cell phone group, and use = 0.01 as the cutoff for a small P-value, would we reject the null hypothesis and conclude the difference between means is greater than zero?

32.A survey for business owners, conducted on a sample of 8 countries, looked at the percentage of businesses in each country that exported goods to China, and the percentage that imported goods from China. Output is shown from carrying out a comparison with software.

33.Percentages of roads classified as bad in 2006 were compared for a sample of 11 northern cities and a sample of 4 southern cities.

34.A student compared tuition, in thousands of dollars, for samples of public and private colleges/universities in the U.S.

35.Short-term parking rates were compared for a sample of 11 parking lots in a city’s downtown area, in 2007 vs. 2008.

36.A masters thesis by M. Purser at the University of Washington in 1988 looked at soil densities in a conifer forest, before and after clearcut logging in the area. These histograms show 32 pre-logging densities and 38 post-logging densities, recorded in grams per cubic centimeter. Unlike most before-and-after designs, this was a two-sample study: the same sample of soil could not be assessed twice.

First compare the histograms’ centers: when were the densities higher on average?

37.Is there a difference in mean hotel rates (five-night stay) for all hotels in Jamaica Curacao, and St. Lucia? Analysis of variance was carried out on samples of hotels a each of the three resorts:

38.Is there a difference in mean hours slept for students in various years (1, 2, 3, 4, or other) at college? Analysis of variance was carried out on survey data from several hundred students at a certain university:

As far as the sample means are concerned, which group of students slept the longest?

39.Prices for samples of 16 new fiction, 16 non-fiction, and 10 advice books (all hardcover) were compared to determine if the overall mean price could be the same for the three types of book.The mean of any F curve is close to 1. What does the size of your F statistic suggest about the size of the P-value?

40.Miles driven (in thousands) were regressed on year for a sample of used Ford Mustangs.

41.Prices of a sample of generic drugs were regressed on the prices of the brand-name equivalents.

42.Which of these is true about the confidence interval (C.I.)?

43.A newspaper surveyed its readers about all of its comics, where possible responses were love it, hate it, or don’t care. The count of readers who responded “hate it” was regressed on the count who responded “love it” for a sample of 6 comics (Foxtrot, Zits, Blondie, Mary Worth, The Amazing Spider Man, and Family Circus).

44. An annual state assessment test is a standards based criterion-referenced assessment used to measure a student’s attainment of the academic standards while also determining the degree to which school programs enable students to attain proficiency of the standards. For a sample of schools, three relationships are considered: percentage passing versus school mean score, percentage passing versus percentage who participated (took the test) in each school, and percentage passing versus percentage of disadvantaged students in the school. In this exercise, you are to identify which one of the three reported regression results corresponds to each of the three scatterplots. 95% confidence interval for β1 for regression of % passing on mean (plot on the left)

45.regression line for regression of % passing on mean (plot on the left)

46.spread s about the line for regression of % passing on mean (plot on the left)

47.spread s about the line for regression of % passing on participated (plot in the middle)

48.t statistic to test if β1 = 0 for regression of % passing on participated (plot in the middle)

49.Scientists believe people’s ears get larger with age. They measured ear length in a sample of patients, aged 30 to 93, and found their ears grew about 0.01 inches a year.What type of study was this?

50.The explanatory variable is

**BA 215/ BA215 WEEK 1 ASSIGNMENT**

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Question 1

Determine which of the following statements is descriptive in nature and which is inferential. Refer to the data below in How Old is My Fish?

a. All 9-inch largemouth bass in New York State are an average of 3 years old

b. Of the largemouth bass used in the sample to make up the NYS DEC Freshwater Fishing Guide, the average age of 9-inch largemouth bass was 3 years.

In your answer also describe and explain the difference between descriptive statistics and inferential statistics

Question 2

Since 1981, Fortune magazine has been tracking what they judge to be the “best 100 companies to work for.” The companies must be at least ten years old and employ no less than 500 people. Below are the top 25 from the list compiled in 1998, together with each company’s percentage of females, percentage of job growth over a 2 year span, and number of hours of professional training required each year by the employer

a. Find the mean, range, variance, and standard deviation for each of the three variables shown in the list. Present your results in a table

b. Using your results from (a), compare the distributions for job growth percentage and Percentage of women employed

**BA 215/ BA215 WEEK 1 DISCUSSION WHY STUDY STATISTICS**

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Hello Class! For this discussion you can choose which question you respond to. Feel free to respond to both, however only one is required. Please respond to one of the following questions:

Question A

Tell us about yourself so you can meet and greet other fellow Grantham University students within your course. Include what you believe to be your current knowledge level of this course topic and what you hope to learn before the course is over.

Question B

Write a 200 word essay/explanation on why you should study statistics. In your answer define the word statistics and discuss how you will use statistics in your career field.

**BA 215/ BA215 WEEK 2 ASSIGNMENT**

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Question 1

Baseball stadiums vary in age, style, size, and in many other ways. Fans might think of the size of the stadium in terms of the number of seats, while the player might measure the size of the stadium by the distance from the homplate to the centerfield fence. Note: CF = distance from homeplate to centerfield fence.

Using the Excell add-in construct your scatter diagram with the data set provide below

Is there a relationship between these two measurements for the “size” of the 30 Major League Baseball stadiums

a. Before you run your scatter diagram answer the following: What do you think you will find? Bigger fields have more seats? Smaller fields have more seats? No relationship exists between field size and number of seats? A strong relationship exists between field size and number of seats? Explain

b. Construct a scatter diagram and include it in your answer.

c. Describe what the scatter diagram tells you, including a reaction to your answer in (a).

Question 2

Place a pair of dice in a cup, shake and dump them out. Observe the sum of dots. Record 2, 3, 4, _ , 12. Repeat the process 25 times. Using your results, find the relative frequency for each of the values: 2, 3, 4, 5, _ , 12

**BA 215/ BA215 WEEK 2 DISCUSSION IDEAL STATISTICIAN**

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Business professionals who use statistics are not mere number crunchers who are “good at math.” As Jon Kettenring succinctly said, “Industry needs holistic statisticians who are nimble problem solvers” (www.amstat.org).

Consider the criteria listed below:

The ideal statistician

Is technically current (e.g., software-wise)

Communicates well

Is proactive

Has a broad outlook

Is flexible

Focuses on the main problem

Meets deadlines

Knows his/her limitations and is willing to ask for help

Can deal with imperfect information

Has professional integrity

Locate an individual in your company who exemplifies these characteristics and interview them on the importance of understanding statistics and the challenges they may face with data. Ask them how they demonstrate these characteristics in their job.

You may summarize your interview in a brief narrative (250–500 words) or you may audio/video record the interview and upload it for viewing to the discussion forum.

**BA 215/ BA215 WEEK 3 ASSIGNMENT**

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1. If you could stop time and live forever in good health, what age would you pick? Answers to this question were reported in a USA Today Snapshot. The average ideal age for each age group is listed in the following table, the average ideal age for all adults was found to be 41. Interestingly, those younger than 30 years want to be older, whereas those older than 30 years want to be younger

2. Find the area under the normal curve that lies to the left of the following z-values

**BA 215/ BA215 WEEK 3 DISCUSSION DECEPTIVE STATISTICS**

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There are examples of deceptive statistics everywhere — visual data presentations (charts/graphs) — from magazines to newspaper articles. Locate a particularly outrageous chart/graph and interview people in your company about the message they interpret from this example. Ask them the purpose of the statistics/research–chart/graph, the strengths and weaknesses of the chart/graph and if are they convinced or suspicious of its findings. What would they recommend to make the results more credible (if anything). Make an audio or video clip of your interview and upload it to this cite. Be sure to include a picture of the graph in the discussion forum.

**BA 215/ BA215 WEEK 4 DISCUSSION STATISTICS PITFALLS**

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As a person who understands and uses statistics to solve problems in business you know that you must use the right statistical tool to compare data against theories. If the data doesn’t support the theory under investigation, you either reject or revise your theory. (You don’t revise the data!)

However, you understand that pitfalls may exist in the data collection process and the reasoning process. For instance, you know to watch for:

1.Making conclusions about a large population from a small sample.

2.Making conclusions from nonrandom samples

3.Attaching importance to rare observations

4.Using poor survey methods

Working with someone in class or in your company…explain/discuss each pitfall and how it might impact good problem solving in the business environment. You may write a short narrative of 250–500 words or you may create an audio/video file to be viewed by members of the class.

You must read, listen or view 2 other students presentations and in your response — indicate how their answers are the same or different from yours.

**BA 215/ BA215 WEEK 4 PROCTORED ASSESSMENT MID-TERM EXAM**

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1. Older people who walk quickly live longer explains that researchers in 2005 used measurements of walking speed from data collected in 1996 from about 500 elderly people. National mortality information enabled the researchers to check on whether the people were still alive nine years later. They found that 27 percent of people deemed to walk at a fast speed in 1996 (about 2.5 miles per hour) were dead nine years later. Meanwhile, 77 percent of those evaluated as walking slowly (less than 1.5 mph) had died, as had 50 percent of those at medium speed.

What type of study was this?

2. Researchers have recently studied the phenomenon of “Chemo brain”, whereby chemotherapy drugs for breast cancer presumably cause women to experience loss of some cognitive ability.The report also claimed that 15% of the nation’s 2.4 million female breast cancer survivors remain distracted years after their chemo-therapy treatment. This result was most likely based on

3. Ever since Scrooge in Dickens’ A Christmas Carol blamed his sleep disturbances on “a crumb of cheese”, there has been a common belief that cheese can cause nightmares. The British Cheese Board carried out a study in 2005 that attempted to dispel such rumors. A group of 200 volunteers were asked to eat 20 grams of cheese 30 minutes before going to sleep each night for a week, afterwards, none of the participants reported having had nightmares, 72% reported having slept very well every night.The response variable’s type is

4. The design described is

5. Another possible design would be to survey a large group of people, asking them about their cheese consumption before bed and about their dreams/nightmares. A weakness of this design is

6. Suppose researchers want to test the theory that an apple a day keeps the doctor away, and carry out a study in which a group of 20 patients has their health assessed initially. They are instructed to eat an apple every day for a month, after which their health is reassessed to see whether or not it has improved overall.The design described is

7. See erotic picture, bet big money, researchers contend reports that “when young men were shown erotic pictures, they were more likely to make a larger financial gamble than if they were shown a picture of something scary, such as a snake, or something neutral, such as a stapler…”To summarize their results, the researchers would compare

8. Carnegie Mellon researchers recently conducted a study in which they influenced participants’ perceptions of their wealth by asking a question about annual income in a general survey. The first group was made to feel poor by asking the individuals to report their income on a scale that began at “less than $100,000” and increased in $100,000 increments, so that most respondents were in the lowest tier. The second group was made to feel subjectively wealthier by asking them to report income on a scale that began with “less than $10,000” and increased in $10,000 increments, so that most respondents were in a middle or upper tier. “Participants received $5 for taking the survey and then were given the chance to buy up to five scratch-off lottery tickets. Those in the first group bought an average of 1.27 tickets compared to 0.67 tickets bought by the second group.”What variable types are involved?

9. The New York Times reports: “The older a man is, the more likely he is to father children who develop bipolar disorder as adults, a large Swedish study reports.Previous studies have found an association between paternal age and both autism and schizophrenia, but this is the first time a connection with bipolar illness has been suggested. The study appears in the September issue of The Archives of General Psychiatry.The researchers examined highly accurate Swedish government health records of more than seven million people with known biological parents to find 13,428 with bipolar disorder diagnosed at two or more separate hospital admissions. They matched each case with five controls, people of the same age and sex but without bipolar illness. They divided the fathers into five-year age categories beginning at 20.After statistically adjusting for the age of the mother, family history of psychotic disorders, education level and other factors, they found consistently increasing risk as fathers aged. The highest risk was in fathers 55 and older. For mothers, after adjusting for the fathers age, they found a statistically significant increase in only the 35 to 39 age group.”Which one of the following was treated as a response variable?

10. “Men with egalitarian attitudes about the role of women in society earn significantly less on average than men who hold more traditional views about women’s place in the world… The comparisons were based on men and women working in the same kinds of jobs with the same levels of education and putting in the same number of hours per week. Men with traditional attitudes about gender roles earned $11,930 more a year than men with egalitarian views…”What is taken to be the response variable here?

11. The Effect of Authority Status on Compliance describes an undergraduate psychology research study which recruited 29 female college students who were asked to complete a questionnaire. Afterwards, the researcher requested that they deliver an envelope to a remote part of campus. In some cases the researcher was made to appear as an authority figure in professional garb with labcoat. In other cases the researcher posed as a non-authority figure in jeans and a T-shirt. The researchers wanted to see if the students were more likely to agree to deliver the envelope if the request was made by the authority figure. Their purpose was to explore the idea that Nazis managed to manipulate people because of their willingness to comply with authority figures.Authority or non-authority status plays what role here?

12. A survey reported that 56% of 5,300 business graduate students admitted having cheated.The number 0.56 is

13. A study by the National Coffee Association found that 83% of the cups of coffee consumed by surveyed Americans were drunk during the morning.The number 0.83 is

14. What is the variable of interest?

15. Of 1,007 firearms recovered by a city’s police bureau’s Firearms Tracking Unit in 2007, only 12% had been reported as stolen.If we use the results to claim that approximately 12% of recovered firearms in the U.S. had been reported as stolen, there may be bias due to

16. The Food and Drug Administration wanted to inspect plants around the world that manufacture drugs to be exported to the U.S. This stemplot shows the percentage of drug plants that the FDA inspected in ten countries that export products to the U.S. Stems represent percents and leaves represent tenths of a percent, the maximum is 12.0 percent.

17. This histogram shows annual per capita spending on bakery products, recorded for 24 U.S. cities in 2006. How do we denote the mean and standard deviation of this data set?

18. The shape is

19. The New York Times reported on the prices of 40 different brands of lipstick. Here is a histogram of the data.

20. Which one of these is a reasonable guess for the standard deviation, which measures typical distance of prices from their mean? (No calculations necessary.)

**BA 215/ BA215 WEEK 5 ASSIGNMENT**

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Question 1

Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits

Question 2

Consider a population with μ = 43 and σ = 5.2.

Calculate the z-score for anx̅ of 46.5 from a sample of size 35.

Could this z-score be used in calculating probabilities using Table 3 in Appendix B? Why or why not?

Question 3

State the null and alternative hypotheses for each of the following:

You want to show an increase in buying and selling of single-family homes this year when compared with last year’s rate. .

You are testing a new recipe for “low-fat” cheesecake and expect to find that its taste is not as good as traditional cheesecake.

You are trying to show that music lessons have a positive effect on a child’s self-esteem.

You are investigating the relationship between a person’s gender and the automobile he or she drives — specifically you want to show that more males than females drive truck-type vehicles

**BA 215/ BA215 WEEK 5 DISCUSSION CLASSICAL HYPOTHESIS TEST**

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**This file of BA 215 Week 5 Discussion Classical Hypothesis Test covers:**

Discuss the “Classical Hypothesis Test: A Five-Step Procedure” on page 173 of your textbook.

1. Write the 5 step procedure

2. Explain the importance of checking for normality in the assumptions in step 2.

3. Why is step 3 so difficult for most statistics students?

4. How do you select the correct test statistic?

5. Can you ever “prove” the alternative hypothesis?

**BA 215/ BA215 WEEK 6 ASSIGNMENT**

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Question 1:

Confidence Interval Formula for μ is as follows:

X — zscoreα/2 * s/√n μ X + zscoreα/2 * s/√n where:

X = sample mean, s = sample standard deviation, zscore = Normal distribution Z-score from a probability where α = (1 — Confidence Percentage)/2

Question 2

An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown below

**BA 215/ BA215 WEEK 6 DISCUSSION NECESSITY OF GOOD WRITING SKILLS**

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Statistics utilizes math and science in its application. So, why do you need to be an effective writer when using statistics?

Working with someone in class or in your company…explain/discuss why you need to be a good writer when problem solving using statistics.

You may write a short narrative of 250–500 words or you may create an audio/video file to be viewed by members of the class.

You must read, listen or view 2 other students presentations and in your response — indicate how their answers are the same or different from yours.

**BA 215/ BA215 WEEK 7 ASSIGNMENT**

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**This pack of BA 215 Week 7 Assignment encompasses:**

To compare commuting times in various locations, independent random samples were obtained from the six cities presented in the “Longest Commute to Work” graphic on page 255 in your textbook. The samples were from workers who commute to work during the 8:00 a.m. rush hour. One-way Travel to Work in Minutes

Construct a graphic representation of the data using six side-by-side dotplots.

Visually estimate the mean commute time for each city and locate it with an X.

Does it appear that different cities have different effects on the average amount of time spent by workers who commute to work during the 8:00 a.m. rush hour? Explain.

d. Does it visually appear that different cities have different effects on the variation in the amount of time spent by workers who commute to work during the 8:00 a.m. rush hour? Explain.

Part 2

Calculate the mean commute time for each city depicted.

Does there seem to be a difference among the mean one-way commute times for these six cities?

Calculate the standard deviation for each city’s commute time.

Does there seem to be a difference among the standard deviations between the one-way commute times for these six cities

Part 3

Construct the 95% confidence interval for the mean commute time for Atlanta and Boston.

Based on the confidence intervals found does it appear that the mean commute time is the same or different for these two cities (Atlanta and Boston). Explain

Construct the 95% confidence interval for the mean commute time for Dallas.

Based on the confidence intervals found in (Atlanta and Boston) and Dallas does it appear that the mean commute time is the same or different for Boston and Dallas? Explain.

Based on the confidence levels found in (Atlanta and Boston) and (Dallas) does it appear that the mean commute time is the same or different for the set of three cities, Atlanta, Boston, and Dallas? Explain

Interstate 90 is the longest of the east-west U.S. interstate highways with its 3,112 miles stretching from Boston, MA at I-93 on the eastern end to Seattle WA at the Kingdome on the western end. It travels across 13 northern states, the number of miles and number of intersections in each of those states is listed below.

Construct a scatter diagram of the data.

Find the equation for the line of best fit using x= miles and y=intersections.

Using the equation found in part (b), estimate the average number of intersections per mile along I-90.

Find a 95% confidence interval for β1.

**BA 215/ BA215 WEEK 7 DISCUSSION ETHICAL GUIDELINES**

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**This pack of BA 215 Week 7 Discussion Ethical Guidelines gives the solution to:**

Go to the website www.amstat.org. Discuss the ethical guidelines that have been extensively reviewed by the statistics profession.

Why are safeguards in plact to protect professional integrity but also to minimize ethical breaches. Why do analysis need to know and follow accepted procedures, maintain data integrity, carry out accurate calculations, report procedures faithfully, and proftectconfidential information?

You may work with a classmate or a person at your place of work to discuss the importance of these questions.

You may write a short narrative of 250–500 words or you may create an audio/video file to be viewed by members of the class.

You must read, listen or view 2 other students presentations and in your response — indicate how their answers are the same or different from yours.

**BA 215/ BA215 WEEK 8 ASSIGNMENT REFLECTION**

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**This paper of BA 215 Week 8 Assignment Reflection comprehends:**

As we wind down this 8 week journey, in 350 words or more, explain how you might view statistics differently and how you will use statistics in your everyday life. Will you apply what you have learned in this course? How?

**BA 215/ BA215 WEEK 8 DISCUSSION REFLECTION**

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Review and reflect on what you learned in the past 8 weeks. What is the most practical and easily applied lesson you learned? What was the hardest to grasp? Why?