Math 124.05

Midterm I Answers

September 25, 2007

Write your answers on blank paper. Use scratch paper to work out your answers first, then write well-organized, correct answers on your answer sheet. If you cannot calculate something exactly (like a quartile), use a reasonable approximation. You may use one page of notes.

  1. The class levels for students in Math 124 are

Class Level / Number
Freshman / 27
Sophomore / 4
Junior / 8
Senior / 11
Other / 6
Total / 56
  1. Are these data categorical or quantitative?
  2. These are categorical data. Each of the 56 students is put into a category.
  3. Draw a graph that summarizes these data.
  1. A normally distributed dataset has a mean of 63 and a standard deviation of 8.4. What range of data contains 95% of the values?
  2. The range would be
  1. The data on an adjoining page shows how men and women performed on the second online quiz.
  2. In this context, which is the explanatory variable and which is the response variable? Are they quantitative or categorical variables?
  3. Gender is the explanatory variable, and it is categorical. Score is the response variable, and it is quantitative.
  4. What would be the best way to summarize these data numerically and graphically?
  5. The numerical summary would be five-number charts for each gender, and the graphical summary would be side-by-side box plots, one box plot for each gender.
  6. Prepare numerical and graphical summaries for these data.
  7. Here are five-number summaries for each gender:

Gender / 1 / 2
min / 17 / 33
Q1 / 50 / 58
median / 67 / 71
Q3 / 83 / 92
max / 100 / 100
  1. Here are side-by-side box plots for the scores for each gender:

  1. Did the two groups perform significantly differently?
  2. Although there is a large overlap in the scores, in four of the five key statistics gender 2 scored higher than gender 1.
  1. On an adjoining page are data for the gender and class level of students in Math 124.
  2. For these data, assume that gender is the explanatory variable and class level is the response variable. Are the variables quantitative or categorical?
  3. Both Gender and Class Level are categorical variables.
  4. Prepare an appropriate numerical summary of these data.
  5. An appropriate summary would be a table of conditional percentages. We begin with a table of counts:

Gender / Freshmen / Sophomore / Junior / Senior / Unclassified / Total
1 / 12 / 4 / 5 / 6 / 4 / 31
2 / 15 / 0 / 3 / 5 / 2 / 25

Then we calculate the table of conditional percentages:

Gender / Freshmen / Sophomore / Junior / Senior / Unclassified / Total
1 / 38.71% / 12.90% / 16.13% / 19.35% / 12.90% / 100.00%
2 / 60.00% / 0.00% / 12.00% / 20.00% / 8.00% / 100.00%
  1. Does one gender contain a significantly higher percentage of advanced students (junior, seniors and unclassified students) than the other?
  2. Gender 1 includes 48% advanced students; gender 2 includes 40%. I would say that this difference is significant.
  1. Here is a scatterplot showing the scores of students on the second and third in-class tests. The regression line and correlation coefficient are shown on the graph.

  1. Are the data positively or negatively related?
  2. Since the regression line slopes up, the data are positively related.
  3. The graph displays . What is the correct value of the correlation coefficient R.
  4. How strongly do you think the data are related? Explain in complete sentences.
  5. The data are weakly related. The correlation coefficient is only 0.55.
  6. If two student scores on Test 2 differ by 20 points, how much would you expect the scores to differ on Test 3?
  7. The slope of the regression line is 0.3482. If two student scores on Test 2 differed by 20 points, then the scores on Test 3 could be expected to differ by points. You could say that the scores on Test 3 would differ by about seven points.
  8. If a student scored 0 on Test 2, find their expected score on Test 3. Explain why this prediction is or is not valid.
  9. The expected score on Test 3 is points. However this prediction is not valid, because the prediction requires extrapolating from the lower end of the data set. Extrapolation of a linear relation beyond the range of the data can be unreliable.

Data for Problem 3
Gender / Quiz 9/11 / Gender / Quiz 9/11
1 / 100 / 2 / 100
1 / 100 / 2 / 100
1 / 92 / 2 / 100
1 / 92 / 2 / 92
1 / 83 / 2 / 92
1 / 83 / 2 / 92
1 / 83 / 2 / 92
1 / 83 / 2 / 83
1 / 75 / 2 / 83
1 / 75 / 2 / 75
1 / 67 / 2 / 67
1 / 67 / 2 / 67
1 / 67 / 2 / 58
1 / 58 / 2 / 58
1 / 58 / 2 / 58
1 / 58 / 2 / 58
1 / 50 / 2 / 50
1 / 50 / 2 / 42
1 / 50 / 2 / 42
1 / 50 / 2 / 33
1 / 50
1 / 42
1 / 33
1 / 33
1 / 17
/ Data for Problem 4
Gender / Level / Gender / Level
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Freshman / 2 / Freshman
1 / Junior / 2 / Freshman
1 / Junior / 2 / Freshman
1 / Junior / 2 / Freshman
1 / Junior / 2 / Junior
1 / Junior / 2 / Junior
1 / Senior / 2 / Junior
1 / Senior / 2 / Senior
1 / Senior / 2 / Senior
1 / Senior / 2 / Senior
1 / Senior / 2 / Senior
1 / Senior / 2 / Senior
1 / Sophomore / 2 / Unclassified
1 / Sophomore / 2 / Unclassified
1 / Sophomore
1 / Sophomore
1 / Unclassified
1 / Unclassified
1 / Unclassified
1 / Unclassified