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-drinkers
9) What is the 99% CI?
EXERCISE 2
Use the cross-tabulation below to answer questions 1-3.
Homeowner or Renter of Respondent Cross-tabulation
WHITE | BLACK | OTHER | TOTAL | |
Homeowner or renter Owns home Pays rent Other | 590 241 23 | 45 57 4 | 27 24 3 | 662 322 28 |
Total | 852 | 106 | 54 | 1012 |
1) 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 & 5
Rap Music (3) Respondent’s Sex Cross-tabulation
MALE | FEMALE | TOTAL | ||
Rap Music (3) Like it Mixed feelings Dislike it | Count % Within Respondent’s sex Count % Within respondent’s sex Count % Within respondent’s sex | 56 15.3% 60 16.4% 250 68.3% | 55 11.1% 109 22.0% 332 66.9% | 111 12.9% 169 19.6% 582 67.5% |
Total | Count % Within respondents sex | 366 100.0% | 496 100.0% | 862 100.0% |
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 percent’s, and marginal values.
SEX | RESIDENCE | SEX | RESIDENCE |
Male Female Female Female Male Female Female Male Female Female Female Male | On-Campus On-Campus On-Campus On-Campus On-Campus On-Campus On-Campus On-Campus On-Campus On-Campus On-Campus On-Campus | Female Female Female Female Male Female Female Female Male Female Female | On Campus On Campus On Campus On Campus On Campus On Campus On Campus On Campus On Campus On Campus On Campus |
6) 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 election
Frequency | Percent | Valid Percent | Cumulative percent | |
Valid Voted Did not vote Not eligible Refused | 659 211 20 5 | 73.2 23.4 2.2 .6 | 73.6 23.6 2.2 .6 | 73.6 97.2 99.4 100.0 |
Total Missing DK NA | 895 3 2 | 99.4 .3 .2 | 100.00 | |
Total Total | 5 900 | .6 100.0 |
10) Use the table below to calculate chi square:
Classical music (3) Education cross-tabulation
Less Than High School | High School of higher | Total | ||
Classical music (3) Like it Mixed Feelings Dislike it | Count % Within education Count % Within education Count % Within education | 35 30.4% 23 20.0% 57 49.6% | 403 54.2% 196 26.3% 145 19.5% | 438 51.0% 219 25.5% 202 23.5% |
Total | Count % Within education | 115 100.0% | 744 100.0% | 859 100.0% |
For each of the problems below:
A) Draw a scatterplot.
B) Calculate Pearson’s r
C) Calculate the y-intercept, slope, and draw a regression line on the scatterplot.
D)Answer the “prediction” problem
E) Calculate r2 and explain what it tells us about the relationship between the variables
F) Calculate the t-ratio for Pearson’s r and determine the level of significance
11) 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) |
33,250 84,500 66,350 58,425 45,600 67,240 77,900 | 5 21 6 7 8 14 10 |
Prediction 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 “real” 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) | “REAL SOCIAL NETWORKING SCORE (Y) |
25 32 16 10 48 22 15 25 34 41 | 20 10 23 19 37 25 41 25 26 18 |
Prediction problem: What is the “real” networking score for a respondent with a virtual networking score of 30?
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Solution: UST LEARNING ENHANCER PROBLEM QUESTIONS SOLUTION