statistics one

  

Determine the skew (if there is any) and explain in words why there is skew for this particular sample. Be sure it is specific to your own study and not just a generic description of what “skew” means. You can do so graphically, algebraically, or just by eyeballing your data set. 

Example of a good answer: “In my study, the mean is significantly greater than the median, which leads me to believe that the data is skewed to the right. This is further confirmed by 2 outliers – Johnny owns 95 pairs of pants and Suzy owns 126. Everyone else in my study owns less than or equal to 30 pairs of pants.”

Example of l of pants” are not in this part of the project, you’re missing the point. And your grade will also be missing the point(s). You MUST show all calculations. 

PART 6: 

 CONCLUSION! This must be a full page in length, NOT including title and/or any other headers or the citations. If you’re not sure if you’ve written a “full page” then do the SMART thing and write slightly more than a full page. Font can be Calibri or Arial size 11. Double-spaced is fine. Doesn’t have to be perfect APA style but all citations must be included and the citations do NOT count as part of the “full page” requirement. Discuss the conclusion of your study. What does your data analysis imply both about your hypothesis and in general? What practical implications are there based on your study? Does there appear to be any sort of significance? Do you feel like you trust the source you used to begin with? Please feel free to include personal commentary based on your own life experience, or other studies you have seen similar to the one you’ve done. If you’d like to research the topic further online, that might help you out. Also, note that while I do appreciate professionalism, I appreciate even more if I can hear your voice in the write-up. 

2

>Sheet

1 How many glasses of water do you drink per day? Juan David Solis 5 Range

1

3 7 Mean 8

.2

7

Median

8

Bin

Bin

Frequency

6 Mode 9 0

-3

3 2 3 2
8

Q1

7

4-7

7

19

7 19
5

Q3

9

8-

11

11

23

11 23
3

IQR

2

12

–

15

15 5 15

5
5

StDev 2.5951288749 16

-16

16 1 16 1
8

m-s More

0
6

m+s 7
9
10 12
16
14

10
12
9

8

7

6

5
8
9
7
7
9

3

7
8
9
10

11

12
9
8
7
9
10
11
12
9
8
9
7
6
5
9
6

Histogram

Bin 0-3 4-7 8-11 12-15 2 19 23 5 1 3
Frequency

Math 2001 Term Project (25 points total)

DUE DATES:

Part 1: 12/12

Part 2: 1/9

The rest: 2/21 e-mailed or 2/25 in person by 6 PM.

PART 1: Hypothesis (2 points) – You must form a hypothesis about something that you find interesting. It must be something easily measurable and numeric and the hypothesis must be based on either supporting or arguing against an outside source – book, tv, online, whatever. Nothing nominal. And nothing too personal that people are not going to be willing to answer, or answer honestly (cough, response bias, cough). Furthermore, it must be about a MEAN ONLY. And you MUST do this BEFORE the data collection. Please be sure to show me your hypothesis before you begin data collection. I also advise you to stick with “greater than” or “less than” hypotheses, as “exact” hypotheses are nearly impossible to support, unless you’re dealing with very small data value ranges or an extremely small population.

Examples of good hypotheses:

· Blahblahblah.com claims that Americans own on average 10 pairs of pants. I believe the actual mean is less than that.

· Some tv personality said that college students are awake for 15 hours per day. I believe the actual mean is less than that.

· My psychology textbook indicated that math professors drink at least 5 shots of tequila per day. I believe the actual mean is greater than that.

Notice how each of these examples would have subjects answering my question with a NUMBER.

Note also that you might want to prepare yourself for questions about measures of variables. For example, “do you count shorts as pants,” or “how many ounces is a shot?”

Examples of bad hypotheses:

· The average American likes the color blue.

· The average college student has at least 3 family members s/he is ashamed of because of their lengthy prison sentences.

Do not be upset if it turns out your hypothesis is unsupported. Life would be pretty boring if we were right 100% of the time.

PART 2: Data Collection (2 points) – You must survey at least 50 people and ask them the question pertaining to your hypothesis. You do not need to write down names. It’s completely anonymous. Please make sure you provide your data set when you hand in the finalized project.

PART 3: Descriptive Analysis (6 points) –

(A) First, tell me your population and sample. Population must correspond to your hypothesis.

(B) Then tell me what type of data you have collected – Nominal, Ordinal, Interval, or Ratio. Explain why.

(C) Then calculate the mean, median, mode, Q1, Q3, range, IQR, and standard deviation of your data, and include a frequency distribution. You can do so on Excel.

(D) Then create an APPROPRIATE histogram for your data. Again, you may use Excel. If you are uncomfortable with Excel, you may create one by hand using crayons, unicorn stickers, and glitter.

PART 4: (2 points) Determine the skew (if there is any) and explain in words why there is skew for this particular sample. Be sure it is specific to your own study and not just a generic description of what “skew” means. You can do so graphically, algebraically, or just by eyeballing your data set.

Example of a good answer: “In my study, the mean is significantly greater than the median, which leads me to believe that the data is skewed to the right. This is further confirmed by 2 outliers – Johnny owns 95 pairs of pants and Suzy owns 126. Everyone else in my study owns less than or equal to 30 pairs of pants.”

Example of a bad answer: “The mean is greater than the median, so it’s skewed to the right.”

PART 5: (6 points) Create a 95% confidence interval for your study BY HAND and explain in words what it actually means as it pertains to your particular study. Again, this MUST be related to your topic. If you are talking about pairs of pants, and the words “pairs of pants” are not in this part of the project, you’re missing the point. And your grade will also be missing the point(s). You MUST show all calculations.

PART 6: (7 points) CONCLUSION! This must be a full page in length, NOT including title and/or any other headers or the citations. If you’re not sure if you’ve written a “full page” then do the SMART thing and write slightly more than a full page. Font can be Calibri or Arial size 11. Double-spaced is fine. Doesn’t have to be perfect APA style but all citations must be included and the citations do NOT count as part of the “full page” requirement. Discuss the conclusion of your study. What does your data analysis imply both about your hypothesis and in general? What practical implications are there based on your study? Does there appear to be any sort of significance? Do you feel like you trust the source you used to begin with? Please feel free to include personal commentary based on your own life experience, or other studies you have seen similar to the one you’ve done. If you’d like to research the topic further online, that might help you out. Also, note that while I do appreciate professionalism, I appreciate even more if I can hear your voice in the write-up. If you’re funny, please don’t hold back. I truly want you to enjoy this process.

Statistics

Hypothesis:

According to Heathline.com say that men older than 19 years must drink an average 13 cups of water per day. I believe that the actual mean is less than that.

Data collection:

The population is students from Johnson and Wales and the sample is the 50 Johnson and Wales students.

Ratio:

Ratio because it is highest level of measurement and has a true zero.

Skewness is a measure of asymmetry of a data set relative to the mean. A data set in which the mean is greater than the median is skewed to the right while a data set in which the mean is less than the median is said to be skewed to the left. We can also determine the skewness of a data set by observing its graph or by calculating the skewness coefficient.

For the data set of the number of glasses of water drank per day, we can determine the skewness by first generating a histogram using Excel. From the shape of the histogram generated by Excel, it seems that the data is slightly skewed to the right. We also compare the mean and the median, and notice that the mean is 8.2, which is greater than the median which is 8.0, and therefore indicating a slight skewness to the right. We can also determine the skewness by observing the skewness coefficient in the Descriptive Statistics table generated by Excel’s Data Analysis Tool Pak. The coefficient of skewness is 0.5444 (to 4 decimal places). We notice that the value of the skewness coefficient. We determine if this skewness coefficient is statistically significant for the distribution. Data is generally said to be highly skewed if it has a coefficient of skewness that is outside the range of -1 to +1 (Ekstrom, 2012; Rayner, 1995). Significantly right-skewed data have coefficient of skewness values more than +1 while significantly less-skewed data have coefficient of skewness less than -1. (Rayner, 1995). The coefficient of skewed data in this case is within the range for a data set that is not skewed.

The value of the coefficient of skewness in this case is not statistically significant. Since the coefficient is a positive value but less than +1, the conclusion we can make is that the data is not skewed and is approximately normal. If we became stricter with our conclusion, then we can say that the data is only slightly skewed to the right (slightly positively skewed).

References

Ekstrom, M. (2012). A general measure of skewness. Statistics & Probability Letters, 82(8),

1559-1568.

Rayner, J.C.W. (1995). Interpreting the skewness coefficient. Communications in Statistics –

Theory and Methods, 24(3), 593-600.