11.2 - Key

Do men and women participate in sports for the same reasons ? One goal for sports participants is social comparison - the desire to win or to do better than other people . Another is mastery - the desire to improve one's skills or to try one's best . A study on why students participate in sports collected data from independent random samples of 67 male and 67 female under - graduates at a large university . Each student was classified into one of four categories based on his or her responses to a questionnaire about sports goals . The four categories were high social comparison - high mastery ( HSC - HM ) , high social comparison - low mastery ( HSC - LM ) , low social comparison - high mastery ( LSC - HM ) , and low social comparison - low mastery ( LSC - LM ) . One purpose of the study was to compare the goals of male and female students . Here are the data displayed in a two - way table : Gende r Goal Femal e Male HSC - HM 14 3 1 HSC - LM 7 18 LSC - H M 2 1 LSC - LM 25 5 13 Female Male HSC - HM 208463 HSC - LM .104 .269 LSC - HM .313 .075 .373 .194 Calculate the conditional distribution ( in proportions ) of the reported sports goals for LSC - LM each gender and fill it in on the table . Write a few sentences comparing the distributions of sports goals for male and female undergraduates . Males appear to be more focused on social comparison than females since those proportions are higher for men than women . Men and women were both fairly evenly split between high and low focus on mastery . Just looking at the numbers , there does appear to be a difference in the distributions .

Do the data provide convincing evidence of a difference in the distributions of sports goals for male and female undergraduates at the university ? HO : There is no difference in the distribution of sports goals of male and female athlete Ha : There is a difference in the distribution of sports goals of male and female athletes Calculate expected counts Check Conditions Female Male HSC - HM 22.5 22.5 HSC - LM 12.5 12.5 LSC - HM 13 13 LSC - LM 19 19 The data came from two independent random samples . We can assume that 67 students is less than 10 % of the female ( and male ) students at the university . All expected counts are at least 5 . 3. Calculate statistic and P - value x2 : 24.898 df: 3 .00002 P - Value : 4. Conclusion statement Since the p - value is less than the significance level of 0.05 , we reject the null hypothesis . There is convincing evidence that there is a difference in the dsitribution of sports goals for males and females at this university . How do U.S. residents who travel overseas for leisure differ from those who travel for business ? The following is the breakdown by occupation : Occupatio n Leisure travelers ( % ) Business

HO : There is not an association between education level and opinion about handgun bans Ha : There is an association between education level and opinion about handgun bans Name the test : Chi - square test for independence Calculate expected counts Less than High School High School Grad Some Colleg e College Grad Postgrad Degree Yes 46.94 86.19 187.36 94 94.29 29 | 7 1 . 71.22 No 69.06 126.81 275.64 138.71 104.78 Check Conditions The data came from a single random sample of adults . 1201 adults is less than 10 % of all adults Calculate statistic and P - value Χ = 8.525 df : 4 P - Value : 0.074 Conclusion statement

Since the P - value of 0.074 is greater than the significance level of 0.05 we fail to reject the null hypothesis . There is not significant evidence that there is an association between education level and opinions on handgun bans . A survey by the National Institutes of Health asked a random sample of young adults ( aged 19 to 25 years ) , " Where do you live now ? That is , where do you stay most often ? " Here is the full two - way table (omitting a few who refused to answer and one who claimed to be homeless ) : Female Male Parents ' home 923 986 Another person's home 144 132 Own place 1294 1129 Group quarters 127 119 Should we use a chi - square test for homogeneity or a chi - square test for independence in this setting ? Justify your answer Independence The data came from just one sample and was categorized based on two characteristics State appropriate hypotheses for performing the type of test you chose HO : There is not an association between gender and where young adults live Ha : There is an association between gender and where young adults live Minitab output from a chi - square test is shown below . Chi - Square Test : Female , Male ing Expected counts are printed below observed counts Chi - Square contributions are printed below expected counts 1 2 3.147 1909 Female

Yes No Cold Neutral Hot 16 38 75 11 18 29 Compare the distributions of hatching status for the three treatments . The proportion of eggs that hatched in cold water ( 59 % ) is less than those that hatched in neutral ( 68 % ) and is less than those that hatched in hot ( 72 % ) . It appears that as the temperature increases , the liklihood of the egg hatching increases . We would have to do a test to see if it is a significant difference . Are the differences between the three groups statistically significant ? Give appropriate evidence to support your answer . ( Do all the steps , show all work ) We will do a x2 test for homogeneity Ho There is no difference in the true proportion of eggs that hatch at different temperatures Ha There is a difference in the true proportion of eggs that hatch at different temperatures Expected Counts 18.63 38.63 71.74 8.37 17.37 32.26 Conditions The data came from a randomly assigned experiment All of the expected counts are at least 5 x2 = 1.703 df = 2 P- value 0.426 Since the P - value of 0.426 is greater than the significance level of 0.05 , we fail to reject the null hypothesis . There is not significant evidence that there is a difference in the proportions of eggs that hatch at different temperatures .