MAT 107 BCCC Class Parameters vs Personal Sample Data Statistics Questions

Sample Data

The resultsfrom the data collection from all last year’s stat classes from Part 1 of the Project is below.  Yourstatistics from Part 1 need to be used as sample data for all the Steps of Part 2.  The parameters below will be used in Steps 2, 3 & 4, along with yours.

Population Mean µ =19.6 (minutes)     Pop. Standard Deviation ? = 10.5 (minutes)(Assume n > 30.)

Your Sample Mean  __________   Your Sample Standard Deviation   s = _____________

List Your 30 Data Values from Part 1 of the project.

MAT107 Intro to Statistics Project
INDEX _________
Distracted Study Time
Name_______________________________________
Project Part 2 due on Sat. March 5
Class Parameters vs. Personal Sample Data
The results from the data collection from all last year’s stat classes from Part 1 of the Project is below. Your statistics
from Part 1 need to be used as sample data for all the Steps of Part 2. The parameters below will be used in Steps 2, 3 &
4, along with yours.
Population Mean µ =19.6 (minutes)
Pop. Standard Deviation σ = 10.5 (minutes) (Assume n > 30.)
Your Sample Mean 𝑥̅ = __________ Your Sample Standard Deviation s = _____________
List Your 30 Data Values from Part 1 of the project.
Step 1: Exploring Your Statistics
Label a normal curve for your data with mean and 3 standard deviations (from Step 5 of Part 1 of the project), the same
for each question, labeling your axis, as you did at the end of Part 1. Be sure to include a title and units of measure.
Then answer the following questions, drawing pictures (shading appropriately), showing all equations for support.
A. What would be your corresponding x – value to a z-score of – 0.56? What percentage of your focused study times
were at, or less than, that score?
B. What would be your corresponding x – value to a z-score of 2.75? What percentage of your focused study times
were at, or more than, that score?
C. What would be your corresponding x – values to z-scores of – 1 and 2? What percentage of your focused study times
were between those scores?
STEP 2: Sampling Distributions
Using the class (population) parameters, label the axes, calculate the mean of the sampling distribution and the standard
error and label the axes with ±3 standard errors. Be sure to include a title and units of measure. Then answer the
following questions using the drawing (with shading & equations).
A. Given the class parameters, what is the probability the average of your times falling where it did, or below?
B. Given the class parameter, between which two points/times did 68% of the classes’ averages fall?
STEP 3: Confidence Interval
A. Construct a 95% confidence interval for the population’s mean study time.
____________ < μ < ____________ or (_______________, _________________) B. If someone were to ask you what this particular confidence interval means, what would you say? STEP 4: Hypothesis Test Test the hypothesis that the population’s mean is different from the sample’s mean value. Use α = 0.05. Null hypothesis (H0): ______________________ Alternative hypothesis (H1): ________________ Type of Test: ____________________________ Critical Value: ___________________________ or P-value: ________________________ Test statistic: ____________ Conclusion: Do you reject the null hypothesis (yes or no)? _________ If someone were to ask what the conclusion means in this particular study, what would you say? MAT107 Intro to Statistics Project INDEX _________ Distracted Study Time Name_______________________________________ Part 1 (Steps 1-5) due by Wed. Feb. 9. STEP 1: Data Collection How many minutes do you sit down and work with dedicated concentration on your homework without interruption? Look at the time when you start. If you stop working to look at a phone message, take a call or a break, stop the time and write it down. If you listen to music while you study, stop the time when you change the music station, find another song or anything other than making progress on your homework. Then start the time again when you get back to your homework, counting it as a separate homework session. Write down the number of minutes for each incident until you have 30 data points (including repeat times). For example (in minutes): Monday 8, 10, 15, 32, Tuesday 2, 12, 45, Wednesday 10, 11, 11, 9, 15, 15, 65 etc. List 30 Data Values Monday Tuesday Wednesday Thursday Friday 3, 3, 13, 4, 11 6, 4, 6, 16, 7, 17 13, 11, 16, 3, 15 6, 7, 12, 5, 3, 12, 13 5, 16, 6, 15, 9, 3, 17 STEP 2: Organizing Data Construct a Grouped Frequency Distribution for the data you collected. Use 5 classes. Show work for Class Width Here The Max is 17 The Min is 3 Then I performed the following calculation find the Class Width and found it to be 2.8 (Max-Min)/5= (17-3)/5= 2.8 Class Limits Class Boundaries Frequency Relative Frequency 3-5 3 - 5.8 9 0.30 Cumulative Frequency 0.30 6-8 5.8 - 8.6 6 0.20 0.50 9 - 11 8.6 - 11.4 3 0.10 0.60 12 - 14 11.4 - 14.2 5 0.17 0.77 15 - 17 14.2 - 17 7 0.23 1 STEP 3: Histogram Construct a histogram for your data set. Be sure to label the axes appropriately and title your graph. Describe the shape of your histogram. STEP 4: More Descriptive Statistics 3 7 17 3 9 17 3 11 3 11 3 12 4 12 4 13 5 13 5 13 6 15 6 15 6 16 6 16 7 16 A. Order your data points in the box above. B. Find the mean, median, and mode. Show work below and write the final answer in the box. MEAN MEDIAN MODE To find the mean I added all the To find the median I used the To find the mode I counted values, which gave me 277 and sorted values, and find the which number was repeated th divided that number by 30. average between the 15 and the most. th 277/30=9.23 16 values. (7+9)/2=8 The mean is: 9.23 The median is 8 The mode is 3 C. Find the 5-number summary, and the IQR for your sample data. Minimum Q1 Q2 Q3 Maximum 3 5 8 13 17 IQR 13-5=8 8 D. Sketch a box plot, including the proper scale for the range of data. Be sure to title your graph and include units of measure. E. Identify extreme values in your data set using the outlier formulas. If you have no outliers, support that conclusion mathematically. In order to fin outliers, I’m going to use the IQR calculated above. If a value is below Q1-1.5*IQR or Q3+1.5*IQR it’s considered and outlier. Then, Lower bound: 5-1.5*8= -7 Upper bound: 13+1.5*8= 25 In conclusion there are no outliers. F. Write a brief Descriptive Statistical Summary and an Inferential Statistical Summary for your data. On average, I get distracted at around 9 minutes, but that statement is somewhat misleading. The reason is that the data doesn’t seem normal or evenly distributed; by looking at the histogram we see that it could have been almost bimodal. A better conclusion is that I get distracted very soon, at around 3 minutes (which is actually the mode) or after 14 minutes. I would also state that my highest focus takes place at 8 to 10 minutes, since I hardly get distracted at that time. STEP 5: Conclusions A. State your average and calculate your standard deviation Show work below. 𝑥̅ ________9.23________ S = _______5.001_________ ̅ Is simply the mean, which was calculated above and it’s 9.23. 𝒙 To find S I made a table with all the middle steps. X 3 3 3 3 3 4 4 5 5 6 6 6 6 7 7 9 11 11 12 12 13 13 13 15 15 16 16 16 17 17 X-Mean -6.23 -6.23 -6.23 -6.23 -6.23 -5.23 -5.23 -4.23 -4.23 -3.23 -3.23 -3.23 -3.23 -2.23 -2.23 -0.23 1.77 1.77 2.77 2.77 3.77 3.77 3.77 5.77 5.77 6.77 6.77 6.77 7.77 7.77 (XMean)^2 38.85 38.85 38.85 38.85 38.85 27.39 27.39 17.92 17.92 10.45 10.45 10.45 10.45 4.99 4.99 0.05 3.12 3.12 7.65 7.65 14.19 14.19 14.19 33.25 33.25 45.79 45.79 45.79 60.32 60.32 Sum Sum/(n-1) St. Dev. 725.367 25.013 5.001 B. Label a normal curve for your data with mean and 3 standard deviations. Be sure to add a title and units of measure. C. According to the Empirical Rule, between which two number of minutes would 95% of your data lie? According to the Empirical Rule, 95% of my data would lie between -0.769 and 19.236. Since time can’t be negative that should be adjusted to 0 and 19.236. D. What would be a very unusually high number of minutes you would spend on your homework? More than 24.237 minutes would be a very unusually high number of minutes I would spend on my homework without interruption. E. How many minutes correspond to a z-score of -1 in your data set? ______4.232________ F. Ask a couple of classmates about their mean & standard deviation. Briefly, discuss any comparisons and conclusions you have come to as a result of this project (online-only class students can discuss with friends and/or relatives or classmates via the Discussions about how often they are distracted from getting work done).

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