Probability & Statistics Exam 1
The following table shows results of a poll asking adults whether they were looking forward to an upcoming football game, looking forward to the commercials, or didn't plan to watch. To find the conditional distribution of "Response" for women, what would be the denominator? Male Female Total Game 279 200 479 Commercials 81 156 237 Won't Watch 132 160 292 Total 492 516 1008
516
Offices sometimes ask coffee drinkers to leave money in a tray to pay for their coffee, but some people cheat. Suppose researchers alternately taped two posters over the coffee station at a certain office. During oneweek, it was a picture of a mountain scene and during theother, it was a pair of staring eyes. They found that the average contribution was significantly higher when the eyes poster was up than when the mountain scene was there a) Identify the Who for this study b) Identify the What for this study c) Identify the larger population
A. Each instance of a coffee drinker who used the coffee station in the particular office B. The total contributions received and the poster present for each case C. All people in honor system payment situations
Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 39.2 inches and standard deviation of 1.9inches. a) What fraction of kindergarten kids should the company expect to be less than 33 inches tall? b) In what height interval should the company expect to find the middle 60% of kindergarteners? c) At least how tall are the biggest 15% of kindergarteners?
A. 0.1 B. between 37.6 and 40.8 C. 41.2
A magazine article examined the impact of an applicant's ethnicity on the likelihood of admission to a school district's magnet schools programs. Those data are summarized in the table. Ethnicity Accepted Waitlist turned away Total Black/Hispanic 61 254 121 436 Asian 55 229 139 423 White 62 217 144 423 Total 178 700 404 1282 a) What percent of all applicants were Asian? b) What percent of the students accepted were Asian? c) What percent of Asians were accepted? d) What percent of all students were accepted?
A. 33% B. 30.9% C. 13% D. 13.9%
Just how accurate are the weather forecasts we hear every day? The table compares the daily forecast with a city's actual weather for a year. Forecast Rain No Rain Rain 26 62 No Rain 7 270 a) On what percent of days did it actually rain? b) On what percent of days was rain predicted? c) What percent of the time was the forecast correct? d) Do you see evidence of an association between the type of weather and the ability of forecasters to make an accurate prediction? Write a brief explanation, including an appropriate graph. e) Is there any evidence of association between the type of weather and the ability of forecasters to make an accurate prediction?
A. 33/365 = 9% B. 88/365 = 24.1 % C. 81.1 % D. chart that shows 78.8% R.C. E. No, because the accuracy rates for forecasting the different types of weather appear to be very close.
Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 39.2 inches and standard deviation of 1.9inches. a) What fraction of kindergarten kids should the company expect to be less than 38 inches tall? b) In what height interval should the company expect to find the middle 70% of kindergarteners? c) At least how tall are the biggest 20% of kindergarteners?
A. 38-39.2/1.9 = -63.2 from chart .2643 turn to percent 26.43 % is your answer B. The middle 70% of kindergarteners are expected to be between 37.2 inches and 41.2 inches. C. The biggest 20% of kindergarteners are expected to be at least 40.8 inches tall.
A magazine article examined the impact of an applicant's ethnicity on the likelihood of admission to a school district's magnet schools programs. Those data are summarized in the table. a) What percent of all applicants were Asian? b) What percent of the students accepted were Asian? c) What percent of Asians were accepted? d) What percent of all students were accepted?
A. 406/1336 = .3038 rounded to 30.4% B. 53/178 = 29.8% C. 53/406 = .1305 rounded to 13.1% D. 178/1336 = .1332 rounded to 13.3%
Just how accurate are the weather forecasts we hear every day? The table compares the daily forecast with a city's actual weather for a year. Forecast Rain No Rain Rain 29 62 No Rain 6 268 a) On what percent of days did it actually rain? b) On what percent of days was rain predicted? c) What percent of the time was the forecast correct? d) Do you see evidence of an association between the type of weather and the ability of forecasters to make an accurate prediction? Write a brief explanation, including an appropriate graph.
A. 9.6% B. 24.9% C. 81.4% D. The graph with RC at 82.9%
a) What is the difference between categorical and quantitative variables? b) Give an example of a categorical variable. Select all that apply. c)Give an example of a quantitative variable. Select all that apply.
A. A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable. B. Dating status, Gender, Religious affiliation C. Number of siblings, Amount of precipitation, Age
Crowd Management Strategies monitors accidents at rock concerts. In their database, they list the names and other variables of victims whose deaths were attributed to "crowd crush" at rock concerts. Here are the histogram and boxplot of the victims' ages for data from a recent one-year period. a) What features of the distribution are seen in both the histogram and the boxplot? b) What features of the distribution can be seen in the histogram that cannot be seen in the boxplot? c) What summary statistic would be chosen to summarize the center of this distribution? Why? d) What summary statistic would be chosen to summarize the spread of this distribution? Why?
A. Essentially symmetric, very slightly skewed to the right with two high outliers at 36 and 48. Most victims are between the ages of 16 and 24. B. The slight increase between ages 22 and 24 is apparent in the histogram but not in the boxplot. It may be a second mode. C. What summary statistic would be chosen to summarize the center of this distribution? Why? D. The IQR would be the most appropriate measure of spread because of the slight skew and the extreme outliers.
Identify each of the following variables as categorical or quantitative. a) Native language b) Number of pets in family c) Distance of commute to work d) Favorite color e Lucky day of the week f) Eye color g) Time worked in week
A. Native language is a categorical variable. Its values are not numerical B. Number of pets in family is a quantitative variable. Its values are numerical C. Distance of commute to work is quantitative variable. Its values are numerical D. Favorite color is a categorical variable. Its values are not numerical E. Lucky day of the week is categorical variable. Its values are not numerical F. Eye color is a categorical variable. Its values are not numerical G. Time worked in week is a quantitative variable. Its values are numerical
Two language majors, Anna and Megan, took exams in two languages. Anna scored 86 on both exams. Megan scored 78 on the first exam and 90 on the second exam. Overall, student scores on the first exam had a mean of 82 and a standard deviation of 7, and the second exam scores had a mean of 73 and a standard deviation of 12. a) To qualify for language honors, a major must maintain at least an 85 average across all language courses taken. So far, which of Anna and Megan qualify? b) Which student's overall performance was better?
A. Only Anna qualifies B. Anna performed better overall
Two language majors, Anna and Megan, took exams in two languages. Anna scored 80 on both exams. Megan scored 76 on the first exam and 94 on the second exam. Overall, student scores on the first exam had a mean of 80 and a standard deviation of 5, and the second exam scores had a mean of 75 and a standard deviation of 13. a) Which of Anna and Megan qualify for language honors? b) Which student's overall performance was better?
A. Only Megan qualifies B. Megan performed better overall
The figure shown is a graph published by Statistics Sweden. It compares Swedish society in 1750 and in 2010 on the numbers of men and women of various ages, using age pyramids. a) In 1750, few Swedish people were old. How does the figure indicate this? b) In 2010, Sweden had many more people than in 1750. How does the figure indicate this? c) In 2010, of those who were very old, more were female than male. How does the figure indicate this? d) In 2010, the largest five-year group included people born during the era of first manned space flight. How does the figure indicate this?
A. Shorter bars toward the top indicate very few old people in 1750. B. The bars are much longer for both men and women in 2010 than in 1750. C. The bars toward the top are longer on the right side. D. From the graph, the longest bars are associated with the 45-49 age group.
The figure shown is a graph published by Statistics Sweden. It compares Swedish society in 1750 and in 2010 on the numbers of men and women of various ages, using age pyramids. a) In 1750, few Swedish people were old. b) In 2010, Sweden had many more people than in 1750. c) In 2010, of those who were very old, more were female than male. d) In 2010, the largest five-year group included people born during the era of first manned space flight.
A. Shorter bars toward the top indicate very few old people in 1750. B. The bars are much longer for both men and women in 2010 than in 1750. C. The bars toward the top are longer on the right side. D. From the graph, the longest bars are associated with the 45-49 age group.
A class of fourth graders takes a diagnostic reading test, and the scores are reported by reading grade level. The 5-number summaries for 15 boys and 9 girls are shown below. Boys 2.8 3.9 4.4 5.2 5.7 Girls 2.4 3.8 4.3 4.8 5.6 a) Which group had the highest score? b) Which group had the greatest range? c) Which group had the greatest interquartile range? d) Which group generally did better on the test? Explain.
A. The boys had the highest score of 5.7 B. The girls had the greatest range of 3.2 C. The boys had the greatest interquartile range of 1.3 D. The boys did better on the reading test, because the median for the boys was higher than the median for the girls.
A class of fourth graders takes a diagnostic reading test, and the scores are reported by reading grade level. The 5-number summaries for 12 boys and 10 girls are shown below. Boys 2.1 3.9 4.4 5.2 5.6 Girls 2.8 3.3 4.1 4.9 5.7 a) Which group had the highest score? b) Which group had the greatest range? c) Which group had the greatest interquartile range? d) Which group generally did better on the test? Explain. e) If the mean reading level for boys is 4.3 and for girls is 4.0, what is the overall mean for the class?
A. The girls had the highest score of 5.7 B. The boys had the greatest range of 3.5 C. The girls had the greatest interquartile range of 1.6 D. The boys did better on the reading test, because the median for the boys was higher than the median for the girls. E. 4.2
Baseball owners believe that the more runs scored, the higher the attendance. Is there evidence that more fans attend games if the teams score more runs? Data collected midway through the season indicate a correlation of 0.825 between runs scored and the number of people at games. Scatterplot from bottom left to upper right, decent spacing a) Does the scatterplot indicate that it's appropriate to calculate a correlation? Explain. b) Describe the association between attendance and runs scored. c) Does this prove that the owners are right, that more fans will come to games if the teams score more runs?
A. Yes, because the relationship between number of runs scored and attendance appears to be straight. B. The association between attendance and runs scored is positive, straight, and moderate. C. No, there is no basis to make a claim of causation.
Baseball owners believe that the more runs scored, the higher the attendance. Is there evidence that more fans attend games if the teams score more runs? Data collected midway through the season indicate a correlation of 0.875 between runs scored and the number of people at games. a) Does the scatterplot indicate that it's appropriate to calculate a correlation? Explain. b) Describe the association between attendance and runs scored. c) Does this prove that the owners are right, that more fans will come to games if the teams score more runs?
A. Yes, because the relationship between number of runs scored and attendance appears to be straight. B. The association between attendance and runs scored is positive, straight, and moderate. C. No, there is no basis to make a claim of causation.
Consider the following data from a small bookstore. Number of Sales Sales People Working (In $1000) ---------------------------------------- 6 16 9 17 13 19 13 20 15 20 16 21 16 22 17 24 18 24 20 25 a) Prepare a scatterplot of Sales against Number of Sales People Working. Choose the correct scatterplot. b) What can you say about the direction of the association? c) What can you say about the form of the relationship? d) What can you say about the strength of the relationship? e) Does the scatterplot show any outliers?
A. choose the scatterplot that goes from bottom left to upper right. B. There is a positive association C. There is a linear association D. There is a very strong association E. No
Consider the following data from a small bookstore People Working Sales (In $1000) 6 13 6 13 8 19 14 20 15 20 16 20 17 20 18 23 19 24 20 25 a) Prepare a scatterplot of Sales against Number of Sales People Working. Choose the correct scatterplot. b) What can you say about the direction of the association? c) What can you say about the form of the relationship? d) What can you say about the strength of the relationship? e) Does the scatterplot show any outliers?
A. pick the scatterplot starting bottom left diagonally upward to the right B. There is a positive association C. There is a linear association D. There is a strong association E. No
A student makes a relative frequency table from counts of colors in a bag of mixed candies. Which of the following tables might show a valid relative frequency table for the data she collects?
Choose the one that adds up to 100%
The Environmental Protection Agency provides fuel economy and pollution information on over 2000 car models. Here is a boxplot of combined fuel economy (using an average of driving conditions) in miles per gallon by vehicle type (midsize car, standard pickup truck, or SUV) for 2012 model vehicles. Summarize the fuel economies of the three vehicle types.
In general, fuel economy is higher in cars than in either SUVs or pickup trucks. The top 50% of cars get higher fuel economy than 75% of SUVs and all pickups. The distribution for pickups shows less spread.
Which of the following is a property of the correlation coefficient?
The correlation between x and y is the same as the correlation between y and x. The sign of the correlation tells us the direction of the association. The correlation is not affected by changes in units or scale. It is always between −1 and 1.
Subway systems sometimes ask passengers to pay the fare unsupervised, but some people cheat. Suppose researchers alternately taped two posters over the ticket station at a certain subway station. During oneweek, it was a picture of a mountain scene and during theother, it was a pair of staring eyes. They found that the average fare was significantly higher when the eyes poster was up than when the mountain scene was there. Identify the Who for this study Identify the What for this study Identify the larger population
Who: Each instance of a passenger who used the ticket station at the particular subway station What: The total fares received and the poster present for each case Population: All people in honor system payment situations