# subsequent cognitive

Complete the following exercises from “Review Questions” located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

1. Chapter 1, numbers 1.8 and 1.9

2. Chapter 2, numbers 2.14, 2.17, and 2.18

3. Chapter 3, numbers 3.13, 3.14, 3.18, and 3.19

4. Chapter 4, numbers 4.9, 4.14, 4.17, and 4.19

Show all relevant work; use the equation editor in Microsoft Word when necessary.

1.9 Recent studies, as summarized, for example, in E. Mortensen et al. (2002). The association between duration of breastfeeding and adult intelligence. Journal of the American Medical Association, 287, 2365–2371, suggest that breastfeeding of infants may increase their subsequent cognitive (IQ) development. Both experiments and observational studies are cited.

(a) What determines whether some of these studies are experiments?

(b) Name at least two potential confounding variables controlled by breastfeeding experiments.

2.14 (a) Construct a frequency distribution for the number of different residences occupied by graduating seniors during their college career, namely

1, 4, 2, 3, 3, 1, 6, 7, 4, 3, 3, 9, 2, 4, 2, 2, 3, 2, 3, 4, 4, 2, 3, 3, 5

(b) What is the shape of this distribution?

3.13 Garrison Keillor, host of the radio program A Prairie Home Companion, concludes each story about his mythical hometown with “That’s the news from Lake Wobegon, where all the women are strong, all the men are good-looking, and all the children are above average.” In what type of distribution, if any, would

(a) more than half of the children be above average?

(b) more than half of the children be below average?

(c) about equal numbers of children be above and below average?

(d) all the children be above average?

3.14 The mean serves as the balance point for any distribution because the sum of all scores, expressed as positive and negative distances from the mean, always equals zero.

(a) Show that the mean possesses this property for the following set of scores: 3, 6, 2, 0, 4.

(b) Satisfy yourself that the mean identifies the only point that possesses this property. More specifically, select some other number, preferably a whole number(for convenience), and then find the sum of all scores in part (a), expressed as positive or negative distances from the newly selected number. This sum should not equal zero.

3.18 Given that the mean equals 5, what must be the value of the one missing observation from each of the following sets of observations? (a) 1, 2, 10

(b) 2, 4, 1, 5, 7, 7

(c) 6, 9, 2, 7, 1, 2

3.19 Indicate whether the following terms or symbols are associated with the population mean, the sample mean, or both means.

(a) N

(b) varies

(c) ∑

(c) n

(d) constant

(e) subset

4. 9 For each of the following pairs of distributions, first decide whether their standard deviations are about the same or different. If their standard deviations are different, indicate which distribution should have the larger standard deviation. Hint: The distribution with the more dissimilar set of scores or individuals should produce the larger standard deviation regardless of whether, on average, scores or individuals in one distribution differ from those in the other distribution.

(a) SAT scores for all graduating high school seniors (a1) or all college freshmen (a2)

(b) Ages of patients in a community hospital (b1) or a children’s hospital (b2)

(c) Motor skill reaction times of professional baseball players (c1) or college students (c2)

(d) GPAs of students at some university as revealed by a random sample (d1) or a census of the entire student body (d2)

(e) Anxiety scores (on a scale from 0 to 50) of a random sample of college students taken from the senior class (e1) or those who plan to attend an anxiety-reduction clinic (e2)

(f) Annual incomes of recent college graduates (f1) or of 20-year alumni (f2)

4.14 (a) Using the computation formula for the sample sum of squares, verify that the sample standard deviation, s, equals 23.33 lbs for the distribution of 53 weights in Table 1.1.

(b) Verify that a majority of all weights fall within one standard deviation of the mean (169.51) and that a small minority of all weights deviate more than two standard deviations from the mean.

4. 17 Why can’t the value of the standard deviation ever be negative?

4. 19 Referring to Review Question 2.18 on page 46, would you describe the distribution of majors for all male graduates as having maximum, intermediate, or minimum variability?