# Statistic project

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S T A T I S T I C S Eleventh Edition by Robert S. Witte and John S. Witte Complete the following exercises and put them into a Word document. Show all relevant work; use the equation editor in Microsoft Word when necessary. 1.8 Indicate whether each of the following studies is an experiment or an observational study. If it is an experiment, identify the independent variable and note any possible confounding variables. (a) A psychologist uses chimpanzees to test the notion that more crowded living conditions trigger aggressive behavior. Chimps are placed, according to an impartial assignment rule, in cages with either one, several, or many other chimps. Subsequently, during a standard observation period, each chimp is assigned a score based on its aggressive behavior toward a chimp-like stuffed doll. (b) An investigator wishes to test whether, when compared with recognized scientists, recognized artists tend to be born under different astrological signs. (c) To determine whether there is a relationship between the sexual codes of primitive tribes and their behavior toward neighboring tribes, an anthropologist consults avail-able records, classifying each tribe on the basis of its sexual codes (permissive or repressive) and its behavior toward neighboring tribes (friendly or hostile). (d) In a study of group problem solving, an investigator assigns college students to groups of two, three, or four students and measures the amount of time required by each group to solve a complex puzzle. (e) A school psychologist wishes to determine whether reading comprehension scores are related to the number of months of formal education, as reported on school transcripts, for a group of 12-year-old migrant children. (f) To determine whether Graduate Record Exam (GRE) scores can be increased by cramming, an investigator allows college students to choose to participate in either a GRE test-taking workshop or a control (non-test-taking) workshop and then com-pares the GRE scores earned subsequently by the two groups of students. (g) A social scientist wishes to determine whether there is a relationship between the attractiveness scores (on a 100-point scale) assigned to college students by a panel of peers and their scores on a paper-and-pencil test of anxiety. (h) A political scientist wishes to determine whether males and females differ with respect to their attitudes toward defense spending by the federal government. She asks each person if he or she thinks that the current level of defense spending should be increased, remain the same, or be decreased. (i) Investigators found that four-year-old children who delayed eating one marshmallow in order to eat two marshmallows later, scored higher than non-delayers on the Scholastic Aptitude Test (SAT) taken over a decade later. 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? 2.17 Are there any conspicuous differences between the two distributions in the following table (one reflecting the ages of all residents of a small town and the other reflect in the ages of all U.S. residents)? (a) To help make the desired comparison, convert the frequencies (f) for the small town to percentages. (b) Describe any seemingly conspicuous differences between the two distributions. (c) Using just one graph, construct frequency polygons for the two relative frequency distributions. *NOTE: When segmenting the horizontal axis, assign the same width to the open-ended interval (65–above) as to any other class interval. (This tactic causes some distortion at the upper end of the histogram, since one class interval is doing the work of several. Nothing is free, including the convenience of open-ended intervals.) Answers on pages 423 and 424. TWO AGE DISTRIBUTIONSAGESMALL TOWN fU.S. POPULATION (2010) (%)65–above105 1360–6453 555–5945 650–5440745–4944740–4438 735–3931730–3427 625–2925720–2420715–1920710–14197 5–9177 0–4 16 7 Total50099% (find the table at the end) 2.18 The following table shows distributions of bachelor’s degrees earned in 2011–2012 for selected fields of study by all male graduates and by all female graduates (a) How many female psychology majors graduated in 2011–2012? (b) Since the total numbers of male and female graduates are fairly different—600.0 thousand and 803.6 thousand—it is helpful to convert first to relative frequencies before making comparisons between male and female graduates. Then, inspect these relative frequencies and note what appear to be the most conspicuous differ-ences between male and female graduates. (c) Would it be meaningful to cumulate the frequencies in either of these frequency distributions? (d) Using just one graph, construct bar graphs for all male graduates and for all female graduates. Hint: Alternate shaded and unshaded bars for males and females, respectively BACHELOR’S DEGREES EARNED IN 2011–2012 BY SELECTED FIELD OF STUDY AND GENDER (IN THOUSANDS)MAJOR FIELD OF STUDYMALESFEMALESBusiness190.0176.7Social sciences 90.6 87.9Education 21.8 84.0Health sciences 24.9138.6Psychology 25.4 83.6Engineering 81.3 17.3Life sciences 39.5 56.3Fine arts 37.2 58.6Communications 33.5 55.2Computer sciences 38.8 8.6English 17.0 36.8Total600.0803.6. (find the table at the end) 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? Note the question came from this book STATISTICS Eleventh Edition by Robert S. Witte and John S. Witte. If you need more information you can use the book. Below are tables for question 2.17 and 2.18. Table for Question 2.17 TWO AGE DISTRIBUTIONS AGE SMALL TOWN U.S. POPULATION (2010) f (%) 65–above 105 13 60–64 53 5 55–59 45 6 50–54 40 7 45–49 44 7 40–44 38 7 35–39 31 7 30–34 27 6 25–29 25 7 20–24 20 7 15–19 20 7 10–14 19 7 5–9 17 7 0–4 16 7 Total 500 99% NOTE: The top class (65–above) has no upper boundary. Although less preferred, as discussed previously, this type of open-ended class is employed as a space-saving device when, as in the Statistical Abstract of the United States, many different tables must be listed. Source: 2012 Statistical Abstract of the United States. Table for Question 2.18 BACHELOR’S DEGREES EARNED IN 2011–2012 BY SELECTED FIELD OF STUDY AND GENDER (IN THOUSANDS) MAJOR FIELD OF STUDY MALES FEMALES Business 190.0 176.7 Social sciences 90.6 87.9 Education 21.8 84.0 Health sciences 24.9 138.6 Psychology 25.4 83.6 Engineering 81.3 17.3 Life sciences 39.5 56.3 Fine arts 37.2 58.6 Communications 33.5 55.2 Computer sciences 38.8 8.6 English 17.0 36.8 Total 600.0 803.6

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