8 - Colorado Mesa University



HW #13 - O and E stuff

For each problem give the table number (critical value), the data number (test statistic), the Yes/No answer, the p-value and its meaning in everyday terms.

1. (IN CLASS) Can you prove that the leading digits of the population of Colorado cities is not uniform? Here is data from a SRS.

|Leading |1 |2 |3 |4 |5 |6 |

|digit | | | | | | |

|Count |11 |7 |9 |15 |12 |6 |

4. (HOMEWORK PROBLEM) Can you prove at the 1% significance level that the number of absences at an elementary school is not evenly distributed throughout the weekday? Here is a SRS of absences.

|day of week |Monday |Tuesday |Wednesday |Thursday |Friday |

|absences |81 |44 |48 |50 |77 |

5. (ALTERNATE HW) Can you prove at the 5% significance level that college student’s day of the week of their births is not evenly distributed? A group of 630 college students picked at random were asked what day of the week they were born on. By giving their date of birth it was easy to look on the Internet to find the day of the week they were born on.

|Sunday |Monday |Tuesday |Wednesday |Thursday |Friday |Saturday |

|62 |108 |99 |104 |95 |101 |61 |

6. (IN CLASS) Can you prove that the leading digits of the populations of Colorado cities do not follow the distribution of leading digits according to Benford’s Law? Under Benford’s Law the distribution would be:

|Leading digit |1 |2 |

|Violent(murder, assault, etc.) |5 |7 |

|Property(burglary, vandalism, etc.) |22 |40 |

|Drugs/Alcohol |33 |52 |

|Domestic Abuse |20 |34 |

|Other |11 |7 |

12. (ANSWER GIVEN) Can we prove at the 10% significance level that there is any relationship between a person’s age group and their favorite fast-food hamburger restaurant?

| |McDonald’s |Burger King |Wendy’s |Other |

|Under 18 |102 |35 |13 |10 |

|18-65 |89 |42 |29 |10 |

|Over 65 |64 |52 |28 |18 |

13. (SOLUTION GIVEN) Can we prove at the 1% significance level that there is any relationship between how well the flower seeds did and brand? Three brands of flower seeds are studied the data is in the table. The conditions were consistent but were different from ideal for these flowers.

| |Brand A |Brand B |Brand C |

|Did not germinate |15 |20 |9 |

|Germinated, but no flowers |29 |30 |19 |

|Germinated, and flowered |91 |120 |66 |

14. (HOMEWORK PROBLEM) Can we prove at the 10% significance level that there is a relationship between what part of Montana a person lives in and their political affiliation? A poll of Montana residents gave the following data.

| |Democrat |Republican |Independent |

|West |39 |17 |12 |

|Northeast |15 |30 |12 |

|Southeast |30 |31 |16 |

15. (ALTERNATE HW) Cancer of the colon is less common in the Mediterranean region than other Western countries. Perhaps it has something to do with lots of olive oil? Can we prove at the 5% significance level that there is some relationship between amount of olive oil in the diet and whether a person ever got colon cancer, rectal cancer, or neither? Italian researchers compared 1953 patients with colon cancer with a control group of 4154 patients.

| |Low Olive Oil |Medium Olive Oil |High Olive Oil |

|Colon Cancer |398 |397 |430 |

|Rectal Cancer |250 |241 |237 |

|No Cancer |1368 |1377 |1409 |

A) What percent had no cancer?

B) What percent had high olive oil use?

C) Find the distribution of cancer for low olive oil use and high olive oil use.

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