**I. Basic statistics for a single variable**

*Course student learning outcome one: Students will be able to perform basic statistical calculations for a single variable up to and including graphical analysis, confidence intervals, hypothesis testing against an expected value, and testing two samples for a difference of means.*

Flight segment | Distance (miles) |
---|---|

Pohnpei-Honolulu | 3087 |

Honolulu-Chicago | 4242 |

Chicago-Asheville | 532 |

Asheville-Chicago | 532 |

Chicago-Tokyo | 6272 |

Tokyo-Guam | 1561 |

Guam-Pohnpei | 1015 |

The table is flight distances for a seven segment journey from Pohnpei to Asheville and back. Use the distance data to answer the following questions.

**Data sheets**

united.gnumeric

united.ods

- __________ Calculate the sample size n.
- __________ Calculate the minimum (quartile 0).
- __________ Calculate the first quartile (Q1).
- __________ Calculate the median (quartile 2).
- __________ Calculate the third quartile (Q3).
- __________ Calculate the maximum (quartile 4).
- Sketch the box plot for the data.

- __________ Calculate the range.
- __________ If the distance data is divided into
**five**classes,

what is the width of a single class? -
Determine the frequency and calculate the relative frequency for the distance data using five classes.

Class upper limits Frequency F Rel. Freq. **Sums:** -
Sketch a
**frequency**histogram for the ratio level distance data, labeling your horizontal axis and vertical axis as appropriate.

- __________ What is the shape of the histogram?
- __________ Calculate the mode.
- __________ Calculate the mean.
- __________ Calculate the sample standard deviation sx.
- __________ Calculate the z-score for 6272.
- __________ Calculate the standard error SE of the sample mean.
- __________ Calculate t-critical for a 95% confidence level.
- __________ Calculate the margin of error E of the sample mean.
- Calculate the 95% confidence interval for the population mean μ:

p(__________ < μ < __________) = 0.95

**II. Basic statistics for paired, correlated variables**

*Course student learning outcome two: Students will be able to perform basic statistical calculations for paired correlated variables.*

Paired data: time in hours versus distance in miles for the seven flight segments.

Flight segment Hours Distance (miles) Pohnpei-Honolulu 10.10 3087 Honolulu-Chicago 8.08 4242 Chicago-Asheville 1.72 532 Asheville-Chicago 1.80 532 Chicago-Tokyo 13.33 6272 Tokyo-Guam 3.67 1561 Guam-Pohnpei 3.72 1015 - _________ For the paired data, calculate the sample size n.
- ______________ Calculate the slope of the linear regression for the data.
- ______________ Calculate the y-intercept of the linear regression for the data.
- ______________ Is the relation positive, negative, or neutral?
- ______________ Calculate the correlation coefficient r for the data.
- ______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
- ______________ Determine the coefficient of determination.
- ______________ Use the slope and intercept to predict the distance that would be flown in six hours of flight time.
- ______________ Use the slope and intercept to predict the time to fly 2300 miles.

**III. Open data exploration and data analysis**

*Course student learning outcome three: Students will be able to engage in data exploration and analysis using appropriate statistical techniques including numeric calculations, graphical approaches, and tests.
*

O'Hare |
Narita | ||
---|---|---|---|

Domestic | International | Domestic | International |

32778 | 3988 | 4019 | 14358 |

34573 | 4198 | 4183 | 15349 |

34426 | 4215 | 4230 | 15790 |

31793 | 3634 | 3893 | 15014 |

33736 | 3996 | 3836 | 15148 |

30621 | 3133 | 3627 | 14342 |

29200 | 3245 | 3888 | 14947 |

24854 | 2994 | 4144 | 15125 |

25816 | 2805 | 3875 | 13598 |

31157 | 3824 | 4701 | 15783 |

31273 | 3479 | 4014 | 14506 |

32103 | 3780 | 4094 | 15011 |

The main airport serving Chicago is O'Hare. Chicago is the headquarters of United Airlines and O'Hare serves as a central hub* for many domestic and international flights. The main airport serving Tokyo is Narita. Tokyo is the headquarters of Japan Air Lines and Narita also serves as a central hub for many domestic and international flights. The data in the tables is the number of flights per month from June 2013 to May 2014 at each airport. Both the domestic and international flights are reported. Aircraft flights include both arrivals and departures. Sources: http://www.transtats.bts.gov/Data_Elements.aspx?Data=2 and http://www.naa.jp/en/airport/traffic.html.

**Provide numeric statistical support for the answers to the following questions.**

- Which airport, if either, is predominantly a domestic hub? Based on what statistical support?
- Which airport, if either, is predominantly an international hub? Based on what statistical support?
- Which airport is busier in terms of all flights? Based on what statistical support?
- Are there outliers in the number of flights per month? If yes, what values are outliers? Provide statistical support.

*Do not simply write down any and all statistics you have ever learned. Answer the questions and then cite the specific statistic, statistics, or charts that support that answer. When citing a statistic or statistics, include both the name of the statistic and the numeric value. If citing a chart, make a sketch of that chart to support your answer.*

*"Airline hubs are airports that an airline uses as a transfer point to get passengers to their intended destination. It is part of a hub and spoke model, where travelers moving between airports not served by direct flights change planes en route to their destinations." - Wikipedia.