Top-Ten Review for 2nd Quartile of Course

Top-Ten Review for 2nd Quartile of Course

1) What is the probability of rolling 5 on a six-sided die thrice in 7 tosses?

2) What is the probability of rolling 5 on a six-sided die at least once in 7 tosses?

3) Network administrators know that incoming server requests follow a Poisson distribution with an expected arrival of 8 incoming packets per minute. What is the probability of receiving 12 incoming packets during a randomly selected minute?

4) Researchers examine 5,780 customer transactions noting the amount of the transaction, the time of day, and the method of payment, hoping to find correlations between purchase amounts and these other variables. Is this research a designed experiment or an observational study?

5) A study administers message therapy to a sample of injured patients and finds that 36% of men and 45% of women improve. A follow-up study of message therapy finds that 60% of men and 65% of women improve. Why is it incorrect to conclude that a higher percentage of women improve with message therapy. Support your answer with frequencies.

6) Consider the scatter plot below. Estimate a correlation coefficient that measures the magnitude of the correlation between the variables.

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7) Roughly estimate a regression line for the data in the scatter plot.

Assume whole-number increments from 0 to 8 along the axes.

8) Suppose Disease X affects 1% of the population. Suppose a diagnostic exam for Disease X has a sensitivity of 80% and specificity of 98%. What is the probability that a patient has Disease X given that the diagnostic is negative?

9) Adult rabbit weights are normally distributed with a mean of 7 lbs and a standard deviation of 3 lbs. If an adult rabbit is selected at random, what is the probability that the rabbit will weigh between 7 and 13 lbs?

10) Adult rabbit weights are normally distributed with a mean of 7 lbs and a standard deviation of 3 lbs. If an adult rabbit is selected at random, what is the probability that the rabbit will weigh between 5.5 and 9 lbs?

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Answers 1) p ≈ 0.078

2) p ≈ 0.72

3) p = ^e

_12! ^·8

≈ 0.048

4) The research exemplifies an observational study since researchers only observe the variables and do not assign subjects to treatment groups.

5) The number of women and men in each study might be a confounding variable. For instance, suppose the first study included 100 men and 1,000 women. Then, the first study shows that 36 men and 450 women improved.

Now suppose the second study included included 1,000 men and 100 women so that 600 men and 65 women improved. Notice that 636 men out of 1,100 improved (about 58%) while only 515 women out of 1,100 improved (about 47%). Thus, assuming message therapy is more effective with women than men is incorrect.

6) r ≈ −0.85

7) ˆ y = −x + 6 is a fair estimate for the regression line. Using formulas, we obtain ˆ y = −0.67x + 5.7.

8) Using a relative frequency of 1,000, Disease X affects 10 patients leaving 990 healthy patients. The test result is negative. To calculate the number of false negatives, multiply 20% by 10. To calculate the true negatives, multiply 98% by 990. p = (0.2·10)+(0.98·990) ² = ₂₊₉₇₀ ² = ₉₇₂ ² ≈ 0.002.

9) By the 2SD Rule, p = 0.475.

10) p ≈ 0.439

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