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Inference for Regression Review Problems for AP Statistics

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By — McGraw-Hill Professional
Updated on Feb 4, 2011

Review the following concepts if necessary:

Problems

  1. You are testing the hypothesis H0: p = 0.6. You sample 75 people as part of your study and calculate that = 0.7.
    1. What is for a significance test for p?
    2. What is for a confidence interval for p?
  2. A manufacturer of light bulbs claims a mean life of 1500 hours. A mean of 1450 hours would represent a significant departure from this claim. Suppose, in fact, the mean life of bulbs is only 1450 hours. In this context, what is meant by the power of the test (no calculation is required)?
  3. Complete the following table by filling in the shape of the sampling distribution of for each situation.
  4. The following is most of a probability distribution for a discrete random variable.
  5. Find mean and standard deviation of this distribution.

  6. Consider the following scatterplot and regression line.
  7. Cumulative Review Problems

    1. Would you describe the point marked with a box as an outlier, influential point, neither, or both?
    2. What would be the effect on the correlation coefficient of removing the box-point?
    3. What would be the effect on the slope of the regression line of removing the box-point?

Solutions

  1. The power of the test is the probability of correctly rejecting a false hypothesis against a particular alternative. In other words, the power of this test is the probability of rejecting the claim that the true mean is 1500 hours against the alternative that the true mean is only 1450 hours.
  2. P(7) = 1 – (0.15 + 0.25 + 0.40) = 0.20.
  3. μx = 2(0.15) + 6(0.25) + 7(0.20) + 9(0.40) = 6.8.

    (Remember that this can be done by putting the X-values in L1, the p(x)-values in L2, and doing STAT CALC 1-Var Stats L1,L2.)

  4.  
    1. The point is both an outlier and an influential point. It is an outlier because it is removed from the general pattern of the data. It is an influential observation because it is an outlier in the x direction and its removal would have an impact on the slope of the regression line.
    2. Removing the point would increase the correlation coefficient. That is, the remaining data are better modeled by a line without the box-point than with it.
    3. Removing the point would make the slope of the regression line more positive (steeper) than it is already.
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