Probability Essentials

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1. Suppose that the UCLA Health Center administrators took a random sample of 635 UCLA students and asked them about various health and lifestyle habits. One question that they asked was, “Within the past month, did you drink alcohol often (more than 3 times a week), sometimes (1 or 2 a week), or never?” The results are in the following two-way table.

Drink often Drink sometimes Never drink
Live off campus 50 100 47 197
Live on campus 111 221 106 438
161 321 153 635

Are students who live off campus more likely to drink than those who live on campus? in other words, is drinking independent of housing choices? Support your answer with the data from the table. Note, to answer this, we're assuming that the proportions you calculate based on the table are very close to the proportions in the population. As it turns out, this is a good assumption for these data.

2. A middle school teacher was curious about the role of parent involvement (attending parent/teacher conferences) and student achievement in Pre-Algebra. She collected data in the following table.

Active parent participation Some parent participation No parent participation
Above grade level 8 3 1 12
At grade level 13 12 3 28
Below grade level 2 12 8 20
23 25 12 60

Are students whose parents actively participate in school conferences more successful in Pre-Algebra than those whose parents do not take an active role? Again, to answer, we must assume that the proportions represented in this table are similar to those in the population. Another way around this is to assume that we will be randomly selecting from the parents and students represented in this table, and understand that the questions we ask are with respect to just these children.

3. Suppose that Proposition ZZ asks voters for additional funding to update school libraries to be high speed internet connected. A sample of 96 registered voters was asked their party affiliation and whether or not they support Proposition ZZ. Results are displayed in the following table. Do we have evidence that party affiliation and position on Proposition ZZ are independent?

Democrat Republic Other
Favor PropZZ 24 18 30 72
Oppose 8 6 10 24
32 24 40 96

For solutions, click here.