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Exam 1 with Answer Key - Applied Probability and Statistics | MA 331, Exams of Probability and Statistics

Material Type: Exam; Professor: Dupree; Class: Applied Probability & Stats.; Subject: Mathematics; University: Athens State University; Term: Fall 2009;

Typology: Exams

2009/2010

Uploaded on 04/13/2010

mgb701
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Modified True-False
Determine whether each of the following statements is a true statement or a false
statement. If it is false, change the underlined word to make it true. (2 points each)
________1. The relative frequency for a particular category is the number of times the
category appears in the data.
False-normal frequency
________2. Bar charts and pie charts are graphical methods that are often used in
summarizing categorical data.
True
________3. Dotplots and stem-and-leaf plots work best for small numerical data sets.
True
________4. Numerical Variables are also known as qualitative values.
False-quantitative
________5. The number of speeding tickets each student in AP Statistics has received is a
numerical variable.
True
________6. The three types of central tendencies are Mean, Median, and Variance.
False-Mean, Median, and Mode
________7. If the upper tail of the histogram is shorter than the lower tail of the histogram,
then the histogram is said to be skewed right.
False-left
________8. A histogram with two peaks is said to be bimodal.
True
________9. The serial number of an IPOD is a numerical variable.
False-categorical
________10. An observational study can result in data that provides evidence for a cause-
and-effect relationship.
False-experiment
________11. A data set is continuous if the values are isolated points on the number line.
False-discrete
________12. Statistical methods, used appropriately, allow us to draw conclusions based
on data.
True
________13. The ONLY way to show cause & effect is with a well-designed, well-controlled
observation.
False-experiment
________14. The population mean is denoted by .
False-
________15. The population mean is the average of al x values in the entire population.
True
________16. The median is nonresistant to the outliers in a data set.
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Modified True-False Determine whether each of the following statements is a true statement or a false statement. If it is false, change the underlined word to make it true. (2 points each) ________1. The relative frequency for a particular category is the number of times the category appears in the data. False-normal frequency ________2. Bar charts and pie charts are graphical methods that are often used in summarizing categorical data. True ________3. Dotplots and stem-and-leaf plots work best for small numerical data sets. True ________4. Numerical Variables are also known as qualitative values. False-quantitative ________5. The number of speeding tickets each student in AP Statistics has received is a numerical variable. True ________6. The three types of central tendencies are Mean, Median, and Variance. False-Mean, Median, and Mode ________7. If the upper tail of the histogram is shorter than the lower tail of the histogram, then the histogram is said to be skewed right. False-left ________8. A histogram with two peaks is said to be bimodal. True ________9. The serial number of an IPOD is a numerical variable. False-categorical ________10. An observational study can result in data that provides evidence for a cause- and-effect relationship. False-experiment ________11. A data set is continuous if the values are isolated points on the number line. False-discrete ________12. Statistical methods, used appropriately, allow us to draw conclusions based on data. True ________13. The ONLY way to show cause & effect is with a well-designed, well-controlled observation. False-experiment ________14. The population mean is denoted by. False- ________15. The population mean is the average of al x values in the entire population. True ________16. The median is nonresistant to the outliers in a data set.

False-resistant ________17. In a sample of size 25 , the median is the average of the 12th^ and 13th values. False- ________18. (^) s^2 is called the sample standard deviation. False-Variance ________19. A trimmed mean is resistant to the outliers in a data set. True ________20. For a data set having a negatively skewed unimodal histogram, the median is larger than the mean. True ________21. When using a 20% trimmed mean, the largest 10% and the smallest 10% of the observations are discarded while computing the mean. False-20% 20% ________22. A z score tells how many standard deviations a value is from the mean. True ________23. The Empirical Rule can only be used when the histogram of the data set can be closely approximated. True Multiple Choice (1 pt each) ________24. Which of the following graphical methods cannot be used on a categorical data set? a. A bar chart. b. A pie chart. c. A stem-and-leaf display d. All of the above methods can be used on a categorical data set. ________25. Which of the following variables yields data that would be suitable for use in a histogram? a. Color of hair b. Brand of stereo c. Gender of an individual d. The time between two consecutive phone calls ________26. Which of the following is a reason to study statistics? a. Being an informed consumer b. Evaluating decisions that affect your life c. Understanding and making decisions d. All of the above are reasons to study statistics. ________27. Which of the following is not a type of sampling bias? a. Cluster b. Under-coverage c. Nonresponse d. Response ________28. A central concern in an observational study is: a. Obtaining a sample at minimum expense b. Obtaining a large sample

c. Roughly 95% of the observations are within three standard deviations of the mean d. Roughly 95% of the observations are within four standard deviations of the mean. Short Answer / Computational Problems: (with possible point values)

  1. Use the following data taken from an AP Stats class final exam. 100 88 74 65 99 93 56 42 24 56 95 32 88 74 88 66 72 73 92 72 86 69 85 72 95 93 51 95 94 95 52 56 87 76 95 84 80 86 42 90 83 77 a. Construct a stem an leaf plot for the data (1 pt) 02 4 represents 24 as score 02 4 03 2 04 2 2 05 1 2 6 6 6 06 5 6 9 07 2 2 2 3 4 4 6 7 08 0 3 4 5 6 6 7 8 8 8 09 0 2 3 3 4 5 5 5 5 5 9 10 0 b. Frequency Table (6 classes) (2 pts) Class Interval Upper and Lower Bounds Frequency Relative Frequency Cumulative Relative Frequency 24-36 23.5-36.5 2 0.048 0. 37-49 36.5-49.5 2 0.048 0. 50-62 49.5-62.5 5 0.12 0. 63-75 72.5-75.5 9 0.21 0. 76-88 75.5-88.5 12 0.29 0. 89-101 88.5-101.5 12 0.29 1. Totals 42 1

c. Draw and label a Frequency Histogram (2 pts)

  1. List and define three different sampling designs. (3 pts)  Cluster sample-population is divided into groups based on location. Then, randomly select a group and sample all individuals in that area.  Stratified random sample-population is divided into homogeneous groups called strata. Individuals are then randomly selected from each strata.  Simple random sample-sampling design in which every individual has an equal chance of being selected or groups of the population all have an equal chance of being selected
  2. Briefly explan the differences between voluntary response bias and nonresponse bias. Give examples of each. (2 pts) For voluntary response, individuals select themselves to be in the sample. An example would be a magazine survey—where subscribers chose to fill the survey out and send it in. Nonresponse bias is a case when an individual is selected to be part of the sample by those who created the sample and the individual can’t be contacted or refuses to respond. An example would be a telemarketing survey who has selected someone to be in the sample, but the person won’t answer.
  3. Given the following randomly generated table, what are the first 5 people to be selected for a 10,000 vacation getaway if the table is read left to right. (2 pts). 90 Vivian 96 Bonnie 101 Marie 106 Rebecca 111 Samuel 91 Patrice 97 Ariel 102 Lane 107 Sarah 112 Tonya 92 John 98 Belle 103 Star 108 Leon 113 Tyler 93 Greg 99 Todd 104 Lenny 109 Chen 114 Trey 95 Allen 100 Frank 105 Ned 110 Sally 115 Alice 1340 9705 9780 3121 0558 9064 6261 1064 8503 1209 0975 4310 2890 5461 2118 9632 5110 6478 9523 3501 3154 0104 1264 9834 0101 2583 1234 1023 4253 1204 0105 2346 2589 0123 2468 0901 2323 2549 8654 7530 0213 8649 9743 1010 2834

Sarah, Ned, Sally, Rebecca, Lane

c. If the smallest value was 4.1 rather than 5.2, how would the sample mean and sample median change? ( DO NOT RECALCULATE—Explain) (1 pt) The sample median would not change because it is resistant to outliers. The sample mean would get smaller.

  1. An Insurance agent is interested in the amount of money paid out in claims involving fire damage. A sample of 20 claimes were selected and the amount offire damage for each claim is listed below in thousands of dollars. ( 1 pt each) a. Compute 51.9=$52, b. Compute sample median. 53 c. Compute the 10% trimmed mean. 20(0.1)=2 trimmed mean=51.56= d. Compute the sample variance and the sample standard deviation. (you may use the calculator) Standard deviation=19.65=20 sample variance=385. e. Draw the boxplot for the given data. Med: 53 Q1=(36+39)/2=37.5 Q3=(62+65)/2=63.5 IQR= Outer fence: 37.5-3(26)=-40.5 Inner fence: 37.5-1.5(26)=-1. 63.5+3(26)=141.5 63.5+1.5(26)=102. f. Is the observation 13 an outlier? no
  2. The Montana Highway Patrol is studying the speed of automobiles on interstate highways in Montana. A large sample of car speeds was collected using radar and is summarized in the boxplot below. (1 pt each)

a. Determine the lower quartile, sample median, and upper quartile from the boxplot. Lower quartile=75 upper quartile=90 sample median= b. Determine the sample Interquartile range from the boxplot. IQR=90-75= c. Describe the general shape of the distribution of speed suggested by this boxplot. Skewed to the right d. Would a speed of 100 be considered an outlier based upon the information in the above boxplot? no

  1. The average playing time of compact discs in a large collection is 35 min. and the standard deviation is 5 min. a. What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean? (1 pt) 1 standard deviation above: 1=(x-35)/5 x=40 min 1 standard deviation below: -1=(x-35)/5 x=30 min 2 standard deviations away: +/- 2=(x-35)/5 x=25 min and 45 min b. Without assuming anything about the distributions of times, at least what percentage of the times are between 25 and 45 minutes? 100% c. Without assuming anything about the distributions of times, what can be said about the percentage of times that are either less than 20 minutes or greater than 50 minutes? (1 pt) Not enough information