MAD moms of Pohnpei cover photo

The Mile-A-Day moms were recently covered in the Kaselehlie Press. MAD moms commit to running, or walking depending on their own physical capacities, a mile a day for 41 consecutive days. If they skip a day, they start their count over. Originally comprised primarily of mothers with heritages here on Pohnpei, the movement has grown to over 350 participants organized into subgroups such as MAD moms of Kapinga, Pingelap, Mwoakilloa, Texas, Yap, RMI, and Chuuk. Currently the MAD moms are engaged in a 37 day run streak from Thanksgiving to the New Year.

The first section of this final examination uses the average number of miles per day being run by fifty active member of the MAD moms. The data suggests that the MAD moms, on average, complete more than a mile a day. The data is in the following table. Use all fifty data values in the five columns and ten rows of this table.

Miles per day for fifty participants

1.55	2.51	1.03	1.03	1.21
1.63	1.44	1.07	1.50	0.96
1.78	1.34	1.11	1.86	1.44
1.93	2.08	1.32	1.65	1.34
1.78	1.30	1.55	1.04	1.87
1.12	1.59	0.99	1.16	1.55
1.64	1.30	1.53	1.08	1.34
1.85	3.20	1.98	1.39	1.24
0.81	1.69	1.52	1.13	1.36
1.26	1.32	1.58	1.59	1.21
  1. What level of measurement is the mileage data?
  2. Calculate the sample size n:
  3. Calculate the minimum:
  4. Calculate the first quartile Q1:
  5. Calculate the median:
  6. Calculate the third quartile Q3:
  7. Calculate the maximum:
  8. Calculate the range:
  9. If the data is divided into five classes, calculate the width of a single class. Do NOT round this value off!:
  10. Calculate the class upper limits and the frequencies for the data using five classes. Use these results to choose the correct frequency histogram.
    MAD moms of Pohnpei cover photo
  11. What is the shape of the histogram?
  12. Calculate the mode:
  13. Calculate the mean:
  14. Calculate the sample standard deviation sx:
  15. Calculate the standard error SE of the sample mean:
  16. Calculate the degrees of freedom:
  17. Calculate t-critical for a 95% confidence level:
  18. Calculate the margin of error E of the sample mean:
  19. Calculate the lower bound for the 95% confidence interval for the population mean μ:
  20. Calculate the upper bound for the 95% confidence interval for the population mean μ:

NikePlus postrun screenshot

Some of the MAD moms continue their run streak beyond 41 days. Of interest from a sports science perspective is whether the MAD moms are able to complete their mile faster as their streak continues. In other words, are they gaining fitness and if so, at what rate? The MAD moms use a Nike+ running app on their Android smart phones that reports distance, duration, and pace. Pace is the number of minutes to complete a mile. The smaller the pace, the faster the runner. The following table is for an anonymous MAD mom. The first column is the day of the streak, the second is her time to complete one mile in decimal minutes. The table includes selected data from day one to day 95.

Day	Pace
01	20.4
08	19.3
17	18.2
27	17.1
51	16.3
82	15.8
95	14.1
  1. For the paired data, calculate the sample size n:
  2. Rounded to three decimal places, calculate the slope of the linear regression for the data.
  3. Calculate the y-intercept of the linear regression for the data:
  4. Is the relation positive, negative, or neutral?
  5. Calculate the correlation coefficient r for the data. If the correlation is negative, include the negative sign, rounding your answer to two decimal places.
  6. Is the correlation none, weak/low, moderate, strong/high, or perfect?
  7. Rounded to two decimal places, calculate the coefficient of determination:
  8. Use the slope and intercept to predict her pace on the 40th day of her run streak. Round your result to two decimal places:
  9. Use the slope and intercept to calculate the day on which the linear regression predicts she will run a sixteen minute mile. Round to the nearest whole number (the nearest day):

NikeFuel screenshot

Open Data Exploration

The Nike+ running app provides data to the runner on their distance, duration, pace, calories burned, and NikeFuel. NikeFuel is a measure of activity, but Nike will not say how NikeFuel is calculated by the Nike+ running app. Runners are awarded banners for achieving certain NikeFuel milestones. In the above image one can see that I have 224,039 NikeFuel. This open data exploration asks you to determine what running variable the NikeFuel calculation is based on.

The Nike+ running app reports distance (Dis), pace, duration, along with the NikeFuel ("Fuel") earned during a run. This data is reported for 22 runs in the table below.

Is NikeFuel calculated based on the distance, the pace, or the duration (total run time)?

Provide numeric statistical support for your answer to the following questions. Use the single blank to write up your answers to the questions including the statistical support for your answers. Do not just give me a one word answer, give me numeric statistical support for why your answer is correct.

Fuel	Dis	Pace	Duration
1073	2.5	09.82	25.27
3074	7.6	11.53	88.65
2013	4.8	09.58	46.18
0287	0.7	07.77	5.47
1111	2.6	11.6	31.3
1082	2.6	09.97	25.98
3400	8.2	10.32	84.92
1457	3.5	10.73	37.82
1236	2.9	10.07	29.97
2171	5.2	10.82	56.87
0460	1.1	09.85	11.22
0702	1.6	09.00	15.25
2314	5.5	09.97	55.43
0432	0.9	09.95	9.47
2006	4.8	10.17	49.1
1456	3.5	09.88	35
0615	1.4	09.92	14.82
1541	3.7	09.47	35.85
1263	3.0	10.00	30.68
2060	5.0	09.68	49.12
1083	2.6	10.27	26.77
1288	3.2	09.58	30.8

Do not simply write down any and all statistics you have ever learned. Cite specific statistics or charts that support that answer. When citing a statistic or statistics, include both the name of the statistic, the numeric value, and why that statistic is meaningful.