AP Statistics: Chi-Square ( ) Review Problems



AP Statistics: Chi-Square ([pic]) Review Problems Name:____________________________

HW: For each of the following problems, identify the Chi-Square Test (GOF, Independence/Association, or Homogeneity), then find the chi-square statistic, the p-value, and the degree of freedom.

1. Professor Fair believes extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test and the other group could stay as long as desired. The results are shown below. Test at the 0.01 level of significance that the time to do a test and test results are independent.

|Time |A |B |C |F |

|1 hour |23 |42 |65 |12 |

|Unlimited |17 |48 |85 |8 |

2. A sociologist is studying the age of the population in Blue Valley. Ten years ago the population was such that 20% were under 20 years old, 15% were in the 20-35 year-old bracket, 30% were between 36 and 50, 25% were between 51 and 65, and 10% were over 65. A study done this year was a random sample of 210 residents. This sample showed:

|Under 20 |20-35 |36-50 |51-65 |Over 65 |

|15 |25 |70 |80 |20 |

At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

3. The following table shows the results of classifying random samples of 112 librarians and 108 faculty members of the California State University system with respect to gender. Does the data suggest that the librarians and faculty members differ with respect to the proportion of males and females? Test using a 0.05 level of significance.

| |Faculty |Librarians |

|Male |56 |59 |

|Female |52 |53 |

4. Each driver in a sample of size 1024 was classified according to both seat-belt usage and gender. The results are shown below. Does the data suggest an association between gender and seat-belt usage? Use a 0.05 significance level. (This was done in 1977!!)

|Gender |Seat Belt Usage |

| |Don’t use |Use |

|Male |192 |272 |

|Female |284 |276 |

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