1a. Unlike the spinner on p. 90 of the OLI module, imagine a spinner that has on

Question

1a. Unlike the spinner on p. 90 of the OLI module, imagine a spinner that has only 2 colors - - Red and White - - and the colors are the same size. Someone spins the pointer 3 times. List all the possible outcomes of this random experiment. [Use the letters R, W]

1b. What is another name for the list you just made?

2. What is the probability that the color red will come up exactly once in the three spins?

3. What is the probability that red will come up on all three spins?

4. In New York State there is a fairly strong positive correlation between principals’ salaries and the reading scores of their students. (This is true.) Upon learning this, a politician recommends that principals’ salaries be increased because this will cause students’ reading scores to increase. Good idea?

The answer of course was that it was not a good idea at all since association does not imply causation.

Suggest a lurking variable that could reasonably account for the association between students’ reading scores and principals’ salaries. Explain your answer.

[Hint: The lurking variable must be plausibly related to both principals’ salaries and reading scores.]

2. What is the probability that the color red will come up exactly once in the three spins?

3. What is the probability that red will come up on all three spins?

Explanation / Answer

1a. The list of possible outcomes is:

[ RRR, RRW, RWR, WRR, WWR, WRW, RWW, WWW]

1b. This list is also called a sample space.

2)Out of 8 outcomes, red comes exactly once in 3 of them.

Thus required probability = 3/8

3) Red comes on all three spins only one out of 8 times.

thus, required probability = 1/8

4)

A lurking variable is a variable that is not included as an explanatory or response variable in the analysis but can affect the interpretation of relationships between variables. A lurking variable can falsely identify a strong relationship between variables or it can hide the true relationship.

Here,the lurking variable can be the quality of education imparted in the better schools having better facilties and highly qualified and well paid teachers. Highly qualified teachers are well paid and may also have an effect on the results of the students.

Another plausible explanation may be that the principal's pay be based on student's performance. So, better the students perform, higher will the principal be paid.

Hope this helps.

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