Math 138 Summer Section 412- Unit Test 1 Green Form, page 1 of 7

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1 Math 138 Summer Section 412- Unit Test 1 Green Form page 1 of 7 1. Multiple Choice. Please circle your answer. Each question is worth 3 points. (a) Social Security Numbers are illustrations of which of the following types of data: A. Quantitative B. Categorical (b) The mean salary for Teachers in a particular State is $ Assume that these salaries follow a normal distribution. f the standard deviation is $10200 then the salary that corresponds to a "z" score of -1.6 is. A. $40215 B. $25197 C. $37846 D. $50199 (c) The center of a distribution could be summarized using: A. Mean only B. Median only C. Quartiles D. Mean or Median 2. The following data represent the movie lengths in minutes of several Disney movies a) (9 points total) Draw a boxplot of the data. number summary. (5 points ). ~\ (\.~ ~ ~~ ~~ ~~5 ~'\~~ f{"~":_i_l\-----t. i I ]H (4 points). Find (and label) the five Tl: min-64 Q1 = 72.5 med = 75 Q3 = 79.5 max=120 b) Determine the upper fence and lower fence. (2 points) IQR = = QR = 71 - ( 1.5 * 7.) = 62 Q QR = 76 + (1.5 * 7.) = 90

2 Math 138 Summer Unit Test 1 Green Form- page 2 of 6 c) Would a Disney movie which runs 120 minutes be considered an outlier? Why or why not? (3 points; no credit for "yes" or "no".) Such a movie would be considered an outlier because 120 minutes is greater than the upper fence of 90 minutes. d) Give the mean and standard deviation for this data set. (4 points) Mean =78.83 min stdev = min e) Give at least two reasons why this dataset does or does not appear normally distributed. (4 points). Data are skewed (to the right) There is an outlier 3. The Gallup Poll conducted a representative telephone survey of 1017 American voters during December Among the reported results were the voter's gender religion age level of education and party affiliation. Identify thews. (6 points) Who: Voters What: Voter gender religion age level of education party When: December 2012 Where: doesn't say (or USA) How: Telephone survey Why: Doesn't say but perhaps to get an idea of attributes of people of different parties. 4. The distributions of SAT and LSAT scores are both approximately normal and symmetric. Veronica took both tests (at different times) and would like to know on which test her performance was better. Explain your answer. Use z-scores in your explanation. (6 points) Test Veronica's Score Mean Score Standard Deviation SAT LSAT

3 Math 138 Summer Unit Test 1 Green Form - page 3 of 6 SAT z-score is = LSAT z-score is = The LSAT score had the highest z-score and therefore was better. 5. In recent election years political scientists have analyzed whether a "gender gap" exists in political beliefs and party identification. The following table shows data collected from the 2006 General Social Survey on gender and party identification (ID). Party I D by Gender Party Gender Democrat Independent Republican Total Male Female Total a. What percent of the people in this survey are Republicans? Give both the fraction and the percent. (4 points) 764 =0.285 (28.5%) 2681 b. What percent of females are Democrats? Give both the fraction and the percent. (4 points) 567 = (3 7.9%) 1496 c. What percent of the people in this survey are male and Republican? Give both the fraction and the percent. (4 points) 369 = (13.8%) 2681 d. What percent of independents are female? Give both the fraction and the percent. (4 points) 534 = (53.7%) 994

4 Math 138 Summer Unit Test 1 Green Form - page 5 of 6 7? 7. (25 points total) Are the numbers of property crimes in New York State decreasing? Data are provided by the New York State Police for the number of property crimes committed in the state every year from 2000 to To make data entry easier the data were divided by 1000 and rounded. The data are given in the table below. Also given is a plot of the residuals and some output from StatCrunch. Property Crimes Residuals vs. Year Year (1000s) Residuals \ \. / / ; Dependent Variable: Property_ Crimes _(1 OOOs) Independent Variable: Year Property_Crimes_(lOOOs) = *Year Sample size: 10 R (correlation coefficient)= a. Identify the response variable. (1 point) Property Crimes b. Make a scatterplot of the data. (3 points) 48'0 ~b~.~. t.tlo ' <l roq c. Discuss direction form and strength. (3 points) The scatterplot shows a negative direction linear form and very strong. Ye ar

5 Math 138 Summer Unit Test 1 Green Form- page 6 of 6 d. Does the scatterplot suggest that a linear model is appropriate for the data? Explain your answer- no credit for "Yes" or "No". (3 points) Yes- the association is almost perfectly linear. e. Does the plot of the residuals suggest that a linear model is appropriate for the data? Explain your answer- no credit for "Yes" or "No". (3 points) No. The residuals show a pattern. f. What is the linear equation that models the relationship between year and the number of property crimes (in thousands)? (1 point) Property_Crimes_(1000s) = *Year This was given as part of the output. g. State and interpret the slope in context of this problem. (3 points) The slope is (rounded). This means that for every increase of one year in time the number of property crimes decreases by an average of about 11.5 thousand. h. Find the observed number of property crimes for the year (1 point) From the data 381 thousand property crimes were committed in This is the observed value. 1. Find the predicted number of property crimes for the year 2007 (2 points) Property_Crimes_(1 OOOs) = *(2007) = thousand property crimes J. Find the residual for the year (2 points) Residual = Observed -Predicted = = thousand property crimes. k. Interpret the residual for the year (3 points) The regression line overpredicted the actual number of (thousand) property crimes in 2007.