Mathematics Statistics

Chapter 179. Three different drug treatments are used to control hypertension. At the end of treatment, the investigator classifies patients as having either a favorable or an unfavorable response to the medication. Set alpha at .05, and conduct a chi‐square test regarding the null hypothesis of no relationship. If necessary, use the R statistic to determine which cells make a major contribution to the χ 2 . Interpret the findings. If there is evidence of an effect, what is the effect size?Response    I            II                IIIFavorable    70    160    168          398Unfavorable    30    40    32            10210. A psychologist hypothesized that biological males are more likely than biological females to accumulate objects of trivial significance because of a biological basis to acquire and possess. Both male and female students were loaned No. 2 pencils with which to take a multiple‐choice exam. A box labeled “pencils” was positioned next to a table upon which students were to place their answer sheets. The investigator counted the number of males and females who returned the pencils. The hypothesis was that males would be more likely to keep the object. Conduct a chi‐square test to analyze the data. If there is evidence of an effect, what is the effect size?    Kept Pencil    Return PencilMales    15    40Females     38    1711. Specify the correct df for each of these designs.A. 2 × 2B.  3 × 4C. 4 × 5D. 1 × 318. A marketing psychologist is hired as a consultant to an association of recreational vehicle dealers. The dealers would like to know if they should seasonally alter their advertising focus. The psychologist collects data on the number of RVs sold in each season of the year. Conduct a chi‐square test with α = .05 on the following observedfrequencies. Perform follow‐up tests if appropriate. Interpret the findings for the dealers.Spring    Summer    Fall    Winter   160    190    170    130   19. Blow are some data regarding a potential relationship between driving conditions and automobile accidents. Run the appropriate chi‐square test to see if a relationship exists.    Accident    No AccidentRain    29    35No Rain    31    48Chapter 187. The following represents a bivariate distribution, using continuous measures. Convert these scores to ranks. Assign a rank of 1 to the lowest score.X     Y3     72    24     49    128     84     212. Perform a Spearman rank correlation on the ranked data from Problem 12. Can the null hypothesis be rejected if α = .05 for a two‐tailed test?7 review9. researcher would like to examine the correlation between stress and reading comprehension. The researcher randomly selects a sample of nine first‐year college students. Participants are asked to rate their current level of stress on a 1–10 scale, with 1 = no stress and 10 = extreme stress. They are then given a short story to read and a 15‐item comprehension test upon completion of the story. Stress levels and test scores are listed below. What test should be used to measure the relationship and test the null hypothesis of no relationship? Why that particular test? Make a decision regarding the null. Stress level    Test Score2        36        11   9        103        6   10        9               3        4           8        127        149        811. Suppose the biology professor mentioned in the previous question decided to count the number of burps each student generated. Would the test used to analyze the data change? If so, what would be the appropriate test?12. A university administrator looked at the number of senior students majoring in sociology and found 21 out of 24 to be biological females. Assuming the student body at this university is roughly equal in terms of biological sex, what test would the administrator use to see if this academic program is overrepresented with biological females?13 A team of social science researchers wants to know more about social media usage.They are interested in which platforms university students prefer, what type of students use them heavily, and for what social purposes they are used.A.    Think of a research situation that would employa chi‐square test for independence.B.    Think of a research situation that would employ an independent‐samples t test.C.    Think of a research situation that would employ a Wilcoxon signed‐ranks test.14. In fantasy baseball, groups of pretend owners conduct a draft in which they can “buy” baseball players to fill out their roster for an upcoming season. These made‐up teams are then compared based on the individual performance of each team member of each team. At the end of the season, team winners are declared based on the cumulative performance of the roster of players. This practice has become quite popular – and many leagues of friends have stayed together for 20 years or more. Because of some small rule differences between the two leagues within professional baseball, players drafted from National League teams tend to have better defensive numbers, while players drafted from American League teams tend to have better offensive numbers. This opens the door to an interesting question: Is there an advantage to drafting players from one league or the other (all other things being equal) in a fantasy league situation? One way to look at this issue might be to see which made‐up teams have won the fantasy league in the past – teams with predominantly National League players or teams with predominantly American League players. If we had access to this data, describe a methodological situation that would employ the following analytical tools.A.  A chi‐square goodness‐of‐fit testB. A point‐biserial correlationC. A Spearman rank correlation.

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