Statistics for the Behavioral Sciences (calculations)

54.) To determine how well people are complying with the posted speed limits, the State Highway Patrol measured automobile speeds on a section of highway where the posted speed limit is 60mph. For a sample of n=100 cars during daylight hours and good weather conditions, they obtained an average speed of x̄ = 62mph with SS=2475. • Make a 95% confidence interval around the sample mean • Does the confidence interval indicate people were speeding and how can you tell? 55.) Achievement test scores are declining all around us," brooded Professor Probity. "Here are my final exam scores for last year and this year on the same exam." What did Professor Probity discover? This Year Last Year 29 27 27 28 26 25 22 24 19 22 15 20 14 18 10 16 10 12 Ss1=425.15 ss2=226.42 Indicate: a. a statement of your hypotheses in words b. the t-value you compute c. your decision regarding H0 and why, and d. Results of homogeneity of variance test and effect size, if appropriate e. an APA conclusion based on your results 56.) In a group of beginning first graders, a psychologist first formed six matched pairs of children based on their reading readiness scores. One member of each pair was randomly assigned to a reading class, the other to a whole-word class. After 3 weeks of reading instruction, all the children were tested to see how many of a list of 20 new words they could read. The SPSS output is below. Decide whether to reject H0, make an APA conclusion, and tell me what test was used. 57.) A newspaper article reported that the typical American family spent an average of $81 for Halloween candy and costumes last year. A sample of n=16 families this year produced a mean of $90 with SS = 6000. Do these data indicate a statistically significant increase in spending? Use α=.05 Indicate: a. H0 and H1 in words OR symbols b. the t-value you compute c. your decision regarding H0, and d. Results of homogeneity of variance test and effect size, if appropriate e. your APA conclusion based on the results 58.) In a classic study of problem solving, Duncker (1945) asked subjects to mount a candle on a wall in an upright position so that it would burn normally. One group of subjects was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except the tacks and the box were presented separately as two distinct items. The solution to this problem involves using the tacks to mount the box on the wall, which creates a shelf for the candle. Duncker reasoned that the first group would have trouble seeing a “new” function for the box (a shelf) because it was already serving a function (holding tacks). For each subject, the amount of time to solve the problem was recorded. The data are as follows: Box of tacks Tacks and box separate 128 42 160 24 113 68 101 35 94 47 SS = 2746.8 SS = 1066.8 Did subjects who were presented the box and tacks separately take significantly less time to solve the problem? Use α=.05. Indicate: a. a statement of your hypotheses in words OR symbols b. the t-value you compute c. your decision regarding H0 and why, and d. Results of homogeneity of variance test and effect size, if appropriate e. an APA conclusion based on your results 59.) A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each subject ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the subjects began a second 30-day period in which they repeated exactly the same diet except for 2 cups of oatmeal each day. After the second 30-day period, cholesterol levels were measured again. The scores for the 9 subjects were as follows: Subject A. B. C. D. E F G H I 1st score. 145 187 130 155 152 112 120 208 167 2ns score. 145 185 119 140 140 115 111 199 159 Difference. 0 -2 -11 -15 -12 +3 -9 -9 -8 SS=288 Are these data sufficient to demonstrate a significant change in cholesterol level after 30 days with an oatmeal diet? Use α=.05. Indicate: a. the hypotheses in words b. the statistical hypotheses c. t-test, your decision regarding H0, and your conclusion Problem Section—Analyses Using SPSS (60 points) Please use SPSS to compute the test statistic for the following problems. For those questions, please turn in the SPSS output. You can copy and paste the relevant portions of the SPSS output into a Word document, and write your answers to the questions I want you to address for each question below, and then paste it into the area beneath the question. For each question, you must do the following: 1. Perform the appropriate analysis 2. State the null and alternative hypotheses, and 3. Make a decision regarding the null hypothesis and write a statement interpreting your statistical results with regard to the aims of the experiment and as you would write it up in a report, including the statistical evidence to back it up. 4. Also, wherever appropriate, test for the effect size and homogeneity of variance. Write up the results of your findings as you would in a report, using the statistical findings as your evidence. 60.) A friend of yours has been ‘playing’ the stock market. He claims that he has spent years doing research in this area and has devised an empirically successful method for investing. Before you give him money, you evaluate his method. He agrees to a ‘dry run’ during which he will use his method, but instead of actually buying and selling, you just monitor the stocks he recommends to see whether his method really works. During the trial time period, the recommended stocks showed the following price changes (a plus score indicating an increase in price and a minus indicates decrease): (10 points) Stock Price Change ($) A +4.52 B +5.15 C +3.28 D +4.75 E +6.03 F +4.09 G +3.82 During the same time period, the average price change of the stock market as a whole was +$3.25. Evaluate whether his method does better or worse than chance. 61.) One study undertook the effect of parent’s presence on kindergarten-readiness scores of 5-year-old children. The study involved 10 pairs of children matched on the basis of physical maturity (size, weight, physical skills). One child in each pair took a kindergarten-readiness test with a parent present, and the other was tested without a parent. Higher scores indicate greater readiness. What do you conclude? Pair Parent Present Parent Absent 1 28 25 2 19 22 3 22 22 4 24 25 5 23 25 6 34 26 7 20 16 8 19 21 9 23 18 10 24 24 62.) A psychologist believes that the lateral hypothalamus is involved in eating behavior. If so, then electrical stimulation of that area might affect the amount eaten. To test this, 11 rats are implanted with chronically indwelling electrodes. Each rat has two electrodes, one implanted in the lateral hypothalamus and the other in an area where electrical stimulation is known to have no effect. After the animals have recovered from surgery, they each receive 30 minutes of electrical stimulation to each brain area, and the amount of food eaten during the stimulation is measured. The amount of food in grams that was eaten during stimulation is shown below. What do you conclude? (10 points) Lateral Hypothalamus Neutral Area 10 6 18 8 16 11 22 14 14 10 25 20 17 10 22 18 12 14 21 13 21 13 63.) Hoaglin, Mosteller, and Tukey (1981) present data on blood levels of beta-endorphins as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery, and again 10 minutes before surgery. The data are presented below, in fmol/ml. ID 1 2 3 4 5 6 7 8 9 10 12 hrs 10.0 6.5 8.0 12.0 5.0 11.5 5.0 3.5 7.5 5.8 10min 6.5 14.0 13.5 18.0 14.5 9.0 18.0 42.0 7.5 6.0 ID 11 12 13 14 15 16 17 18 19 12 hrs 4.7 8.0 7.0 17.0 8.8 17.0 15.0 4.4 2.0 10min 25.0 12.0 52.0 20.0 16.0 15.0 11.5 2.5 2.0 What do you conclude? 64.) In one of my studies, we tested whether people could estimate accurately when the apex, or highest point a baseball physically reaches in the air, occurs. We predicted that as the landing destination of baseballs approached the observers, they would estimate the apex occurs later than actual. Below is a small sample of our data. Each data point represents one observers’ deviation score for one baseball trajectory, given as: Observers’ estimate – frame when apex actually occurred in time (in terms of 1/30th of a second video frames). What can you conclude? 19.00 19.00 12.00 3.00 16.00 5.00 21.00 11.00 16.00 48.00 15.00 26.00 38.00 30.00 -19.00 33.00 16.00 9.00 16.00 55.00 8.00 24.00 68.00 20.00 24.00 22.00 8.00 20.00 44.00 30.00 26.00 20.00 14.00 22.00 38.00 -1.00 59.00 26.00 22.00 22.00 42.00 3.00 52.00 60.00 7.00 1.00 48.00 20.00 44.00 78.00 40.00 24.00 51.00 19.00 65.) A social psychologist hypothesizes that creation of cognitive dissonance will increase group cohesiveness in discussion groups. Sixteen students are randomly divided into two discussion groups of 8 students each. Dissonance is produced in one but not the other. Afterward the students fill out a questionnaire designed to measure the degree of group cohesiveness. Higher scores = greater cohesiveness. Here are the results: Group Cohesiveness Scores Dissonance Group Nondissonance Group 3 3 8 6 6 4 7 3 5 5 6 2 7 6 6 4 Did dissonance significantly increase group cohesiveness? Problem Section—Analyses Using SPSS (60 points) Stock Price Change ($)