Week of | Minutes |
---|---|

Mon 30 Jun 08 | 139 |

Mon 07 Jul 08 | 189 |

Mon 14 Jul 08 | 239 |

Mon 21 Jul 08 | 137 |

Mon 28 Jul 08 | 302 |

Mon 04 Aug 08 | 143 |

Mon 11 Aug 08 | 348 |

Mon 18 Aug 08 | 103 |

Mon 25 Aug 08 | 224 |

Mon 01 Sep 08 | 165 |

Mon 08 Sep 08 | 226 |

Mon 15 Sep 08 | 186 |

Mon 22 Sep 08 | 234 |

Mon 29 Sep 08 | 293 |

Mon 06 Oct 08 | 113 |

Mon 13 Oct 08 | 358 |

Mon 20 Oct 08 | 133 |

Mon 27 Oct 08 | 322 |

Mon 03 Nov 08 | 152 |

Mon 10 Nov 08 | 346 |

In October 2008 the
United States Department of Health and Human Services
released the first set of
recommendations on physical activity.
The
basic recommendation
is for adults to get 150 minutes of moderately intense activity per week.
The second column of the table indicates the number of minutes of
running per week done by Lee Ling.
Running is one form of intense activity. There are many
others including walking, engaging in sports, strength training, any
activity that raises your heart rate and gets you sweating for at least
twenty minutes a day.
The intensity level of activities varies with the activity and the fitness
of the person. Running is noted to be a *vigorous activity* in an
appendix to the main report.

Use the number of minutes of running per week (**Minutes**) for the following
basic statistics.

- _________ What level of measurement is the data?
- _________ Determine the sample size n.
- _________ Determine the minimum.
- _________ Determine the maximum.
- _________ Calculate the range.
- _________ Calculate the midrange.
- _________ Determine the mode.
- _________ Determine the median.
- _________ Calculate the sample mean x.
- _________ Calculate the sample standard deviation
**sx**. - _________ Calculate the sample Coefficient of Variation.
- _________ Determine the class width. Use
**five**classes (bins or intervals). - Fill in the following table with the class upper limits in the first column, the frequencies in the second column, and the relative frequencies in the third column

Bins (x) | Frequency f | RF p(x) |
---|---|---|

Sums: |

- Sketch a histogram of the relative frequency data.
- __________________ What is the shape of the distribution?
- __________________ On 19 July 2008 I ran in the INS Half-Marathon. That run occurred during the week of 14 July, a week with 239 minutes of running. Use the sample mean x and sample standard deviation sx above to calculate the z-score for 239 minutes of running during the week of 14 July.
- _________ Is the z-score for 239 minutes an ordinary or extraordinary value?
- __________________ On the week of 13 October I racked up 358 minutes of running during the week. I was celebrating 30 years of running – I first ran in 1978. Use the sample mean x and sample standard deviation sx above to calculate the z-score for 358 minutes of running.
- _________ Is the z-score for 358 minutes an ordinary or extraordinary value?
- _________
**Toughie:**How many minutes of running in one week would I have to do in order to attain an exraordinary number of minutes of running in one week? Use z = 2 to find the number of minutes x that I would have to run to reach "extraordinary." - _________ Calculate the standard error of the sample mean x for the number of minutes of running per week.
- _________ Find t
_{critical}for a confidence level c of 95% for the number of minutes of running per week. - _________ Determine the margin of error E for the sample mean x.
- Write out the 95% confidence interval for the population mean μ
for the number of minutes of running per week.

p(_____________ < μ < ___________) = 0.95 - _________ The United States Department of Health recommends 150 minutes of moderately intense activity per week. Use 150 minutes as the population mean μ. Is the number of minutes of running per week done by Lee Ling statistically significantly different than the μ = 150 minutes recommendation?
- ______________________ Using Lee Ling's data above and a population mean μ = 150, determine the t-statistic.
- ______________________ Using Lee Ling's data above and a population mean μ = 150, determine the p-value. Keep three decimal places in your answer.
- ______________________ Using Lee Ling's data above and a population mean μ = 150, determine the maximum confidence interval c for which the difference is statistically significant. Keep three decimal places in your answer.
- _________ Is Lee Ling exceeding the United States Health department minimum physical activity minutes per week guidelines by a statistically significant amount?

Last spring term I was lazy and my running slacked off. My weekly minutes of running was low, some weeks I did not run at all. With the end of the school term in mid-May I planned to put myself on a stricter regimen of running. With only six weeks of renewed effort by the week of 23 June, could I prove that my running duration in minutes per week had improved? Use a t-test for a difference of two independent sample means in this portion of the test. The samples means are the weekly minutes of running for spring versus summmer. Note that for two of my weeks in spring the total weekly running time was actually zero minutes. I did not run during those two particular weeks.

Date | Spring minutes (x) | Date | Summer minutes (y) |
---|---|---|---|

Mon 25 Feb 08 | 194 | Mon 19 May 08 | 331 |

Mon 03 Mar 08 | 0 | Mon 26 May 08 | 182 |

Mon 10 Mar 08 | 141 | Mon 02 Jun 08 | 261 |

Mon 17 Mar 08 | 238 | Mon 09 Jun 08 | 187 |

Mon 24 Mar 08 | 86 | Mon 16 Jun 08 | 207 |

Mon 31 Mar 08 | 88 | Mon 23 Jun 08 | 176 |

Mon 07 Apr 08 | 80 | ||

Mon 14 Apr 08 | 61 | ||

Mon 21 Apr 08 | 49 | ||

Mon 28 Apr 08 | 58 | ||

Mon 05 May 08 | 104 | ||

Mon 12 May 08 | 0 |

- _________ Calculate the sample mean x number of minutes of running per week during the spring term.
- _________ Calculate the sample mean y number of minutes of running per week during the summer.
- _________ Are the sample means for the two samples
**mathematically**different? - __________________ What is the p-value? Use the difference of means for
**independent samples**TTEST function to determine the p-value for this two sample data. Keep three decimal places in your answer. - __________________ Is the difference in the means statistically significant at a risk of a type I error alpha α = 0.05?
- __________________ Would we "fail to reject" or "reject" a null hypothesis of no difference in the means?
- __________________ What is the maximum level of confidence we can have that the difference is statistically significant? Keep three decimal places in your answer.

Data table

Minutes of running | Total daily steps |
---|---|

34 | 10101 |

49 | 14200 |

41 | 8660 |

24 | 8675 |

34 | 10864 |

65 | 15489 |

60 | 14690 |

74 | 14725 |

114 | 18660 |

50 | 16763 |

In October 2008 my last pedometer that could withstand running and rain finally failed. Without a pedometer, can minutes of running be used to estimate daily total steps? Running is very regular and produces, for Lee Ling, 154 steps per minute. The complication is before Lee Ling runs each day he walks around campus. Can a linear regression be used to predict total daily steps just from his daily run? This section explores this question.

- _________ Calculate the slope of the linear regression (best fit line).
- _________ Calculate the y-intercept of the linear regression (best fit line).
- _________ Is the relation between minutes of running and total daily steps positive, negative, or neutral?
- _________ Calculate the linear correlation coefficient r for the data.
- ______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
- ______________ Determine the coefficient of determination.
- ______________ What percent in the variation in the minutes of running "explains" the variation in the total daily steps?
- _________ Use the slope and intercept to predict the number of total daily steps for 100 minutes of running.
- _________ Use the slope and intercept to determine the number of minutes of running required to produce 12000 steps.
- _________ On a day on which I do not run, how many steps am I predicted to get?

For a retrospective look at pedometer data, see also the pedometer mini-studies.