# UST LEARNING ENHANCER PROBLEM QUESTIONS SOLUTION

We sample 20 new cars (sedans) and find the average miles per gallon (mpg) to be 26 with a standard deviation of 1.7.1) If we increase our sample size to 40, what is the standard error of the mean?In a sample of 100 BSC students, we find that on average students eat at a fast-food restaurant four times a week with a standard deviation of .5.2) What is the standard error of the mean?3) If our sample size is 1000, what is the standard error?In a sample of 212 BSC students, we find that 82% are binge drinkers.4) If we increase the sample size to 500, what is the standard error of the proportion?Thirty out of 167 students have been involved in a violent conflict in in the past year.5) If 90 students reported a violent conflict, what is the standard error of the proportions?We sample 20 news cars (sedans) and find the average mpg to be 26 with a standard deviation of 1.7.6) What is the 95% confidence interval (CI)In a sample of 100 BSC students, we find that on average students eat at a fast-food restaurant four times a week with a standard deviation of .5.7) What is the 95% CI?8) What is the 99% CI?In a sample of 212 BSC students, we find that 82% are binge-drinkers9) What is the 99% CI?EXERCISE 2Use the cross-tabulation below to answer questions 1-3.Homeowner or Renter of Respondent Cross-tabulationWHITEBLACKOTHERTOTALHomeowner or renter Owns homePays rentOther59024123455742724366232228Total8521065410121) How many respondents own a home?2) Of Whites, what percent own a home?3) Which of the three groups is most likely to pay rent?Use the table below to answer questions 4 & 5Rap Music (3) Respondentâs Sex Cross-tabulationMALEFEMALETOTALRap Music (3) Like itMixed feelingsDislike itCount% WithinRespondentâs sexCount% Within respondentâs sexCount% Within respondentâs sex5615.3%6016.4%25068.3%5511.1%10922.0%33266.9%11112.9%16919.6%58267.5%TotalCount% Within respondents sex366100.0%496100.0%862100.0%4) Of females, what percent like a rap music?5) Are males or females more likely to like rap music?Suppose that we want to know if males are more likely than females to live off campus. Use the data below to construct a cross-tabulation table. Be sure to include frequencies, column percentâs, and marginal values.SEXRESIDENCESEXRESIDENCEMaleFemaleFemaleFemaleMaleFemaleFemaleMaleFemaleFemaleFemaleMaleOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusOn-CampusFemaleFemaleFemaleFemaleMaleFemaleFemaleFemaleMaleFemaleFemaleOn CampusOn CampusOn CampusOn CampusOn CampusOn CampusOn CampusOn CampusOn CampusOn CampusOn Campus6) What percent of respondents are male?7) Of females, what percent live off-campus?8) Of those who live off-campus, what percent are female?9) Use the table below to calculate chi-square:Voting in 1992 electionFrequencyPercentValid PercentCumulative percentValid VotedDid not voteNot eligibleRefused65921120573.223.42.2.673.623.62.2.673.697.299.4100.0TotalMissing DKNA8953299.4.3.2100.00TotalTotal5900.6100.010) Use the table below to calculate chi square:Classical music (3) Education cross-tabulationLess Than High SchoolHigh School of higherTotalClassical music (3) Like itMixed FeelingsDislike itCount% Within educationCount% Within educationCount% Within education3530.4%2320.0%5749.6%40354.2%19626.3%14519.5%43851.0%21925.5%20223.5%TotalCount% Within education115100.0%744100.0%859100.0%For each of the problems below:A) Draw a scatterplot.B) Calculate Pearsonâs rC) Calculate the y-intercept, slope, and draw a regression line on the scatterplot.D)Answer the âpredictionâ problemE) Calculate r2 and explain what it tells us about the relationship between the variablesF) Calculate the t-ratio for Pearsonâs r and determine the level of significance11) A researcher wants to learn more about the relationship between the number of miles traveled to work and earnings. She hypothesizes that wealthier employees live outside the city rather than in the city and decides to sample a group of workers from a bank located downtown. She obtains the following data.EARNINGS IN \$ (X)MILES TRAVELED TO WORK (Y)33,25084,50066,35058,42545,60067,24077,9005216781410Prediction problem: How far from the city does an employee earning 50,000 live?12) A researcher wants to investigate the relationship between social networks and virtual social networks. She predicts that large virtual networks will be associated with large ârealâ networks. She develops two networking indices to measure networking that range from 0 to 50. Use the data below to access her hypothesis.VIRTUAL SOCIAL NETWORKING SCORE (X)âREAL SOCIAL NETWORKING SCORE (Y)2532161048221525344120102319372541252618Prediction problem: What is the ârealâ networking score for a respondent with a virtual networking score of 30?