Provide an appropriate response. 1) Define the terms population, sample, parameter and statistic. How does a census compare to a sample?

Transcription

1 Practice Exam 1 Summer 2007 M112 Name Provide an appropriate response. 1) Define the terms population, sample, parameter and statistic. How does a census compare to a sample? 2) Distinguish between qualitative and quantitative data. Give an example for each. 3) Define and give examples for nominal, ordinal, interval, and ratio levels of measurement. Describe the type of statistics which might be reported for each. 4) List five different abuses of statistics and give examples for each. 5) Define random sample. Explain why this is important in design of experiments. Determine whether the given value is a statistic or a parameter. 6) A sample of 120 employees of a company is selected, and the average age is found to be 37 years. A) Statistic B) Parameter 1

2 7) After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45,000 kg of the meat was spoiled. A) Parameter B) Statistic Identify the number as either continuous or discrete. 8) The number of freshmen entering college in a certain year is 621. A) Discrete B) Continuous 9) The number of limbs on a 2-year-old oak tree is 21. A) Discrete B) Continuous 10) The height of 2-year-old maple tree is 28.3 ft. A) Continuous B) Discrete Identify the sample and population. Also, determine whether the sample is likely to be representative of the population. 11) An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. 12) 100,000 randomly selected adults were asked whether they drink at least 48 oz of water each day and only 45% said yes. 13) In a poll of 50,000 randomly selected college students, 74% answered "yes" when asked "Do you have a television in your dorm room?". 2

3 Provide an appropriate response. 14) Histograms and Pareto charts are both bar charts. What is the significant difference between the two? 15) Explain the difference between a frequency distribution and a relative frequency distribution. Comment on the differences on the vertical axis scale. Given the same data set and the same classes, will the shapes of the frequency distribution and the relative frequency distribution be the same? You may draw a diagram to support your answer. 16) Suppose you are comparing frequency data for two different groups, 25 managers and 150 blue collar workers. Why would a relative frequency distribution be better than a frequency distribution? Solve the problem. 17) The following frequency distribution analyzes the scores on a math test. Find the indicated class midpoint or boundaries. The class boundaries of scores interval A) 39.5, 59.5 B) 40.5, 59.5 C) 39.5, 58.5 D) 40.5,

4 Construct the cumulative frequency distribution that corresponds to the given frequency distribution. 18) Days of vacation Frequency A) Days of vacation Cumulative Frequency B) Days of vacation Cumulative Frequency C) Days of vacation Cumulative Frequency D) Days of vacation Cumulative Frequency Use the given data to construct a frequency distribution. 19) On a math test, the scores of 24 students were Construct a frequency table. Use 4 classes beginning with a lower class limit of 60. Score Frequency 4

5 A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer the question. The blood pressure readings were given to the nearest whole number. 20) Approximately what percentage of the people aged had a systolic blood pressure reading between 110 and 119 inclusive? A) 35% B) 3.5% C) 30% D) 0.35% 21) Approximately what percentage of the people aged had a systolic blood pressure reading between 110 and 139 inclusive? A) 74% B) 59% C) 39% D) 89% 22) What common class width was used to construct the frequency distribution? A) 10 B) 9 C) 11 D) 100 5

6 Solve the problem. 23) In a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are shown below. Construct a histogram to represent the data. Use 4 classes with a class width of 10, and begin with a lower class limit of What is the approximate amount at the center? Find the original data from the stem-and-leaf plot. 24) Stem Leaves A) 51, 57, 61, 61, 62, 67, 71, 72, 72, 77, 79, 82, 85 B) 51, 57, 62, 62, 67, 72, 75, 77, 79, 82, 85 C) 52, 52, 55, 61, 61, 62, 67, 71, 71, 82, 85 D) 6, 12, 6, 6, 7, 12, 8, 8, 9, 14, 16, 10, 13, 16 Solve the problem. 25) At the National Criminologists Association's annual convention, participants filled out a questionnaire asking what they thought was the most important cause for criminal behavior. The tally was as follows. Cause Frequency education 15.4 drugs 46.2 family 30.8 poverty 53.9 other 7.7 Make a Pareto chart to display these findings. 6

7 A) B) C) D) Provide an appropriate response. 26) Marla scored 85% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 85 percentile in mathematics. Explain the difference in these two scores. 7

8 Find the mean, median, mode, and midrange for each of the two samples, then compare the two sets of results. 27) The Body Mass Index (BMI) is measured for a random sample of men and women. Interpret the results by determining whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If there is, what is it? Men Women Find the mean of the data summarized in the given frequency distribution. 28) The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. Speed (mph) Cars A) 55.8 mph B) 54.5 mph C) 61.4 mph D) 58.6 mph Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results. 29) When investigating times required for drive-through service, the following results (in seconds) were obtained. Restaurant A Restaurant B A) Restaurant A: 57; ; Restaurant B: 77; ; C) Restaurant A: 57; ; Restaurant B: 56; ; B) Restaurant A: 75; ; Restaurant B: 70; ; D) Restaurant A: 57; ; Restaurant B: 70; ;

9 Solve the problem. 30) The race speeds for the top eight cars in a 200-mile race are listed below. Use the range rule of thumb to find the standard deviation. Round results to the nearest tenth A) 3.4 B) 6.8 C) 7.5 D) 1.1 Solve the problem. Round results to the nearest hundredth. 31) Scores on a test have a mean of 73 and a standard deviation of 9. Michelle has a score of 91. Convert Michelle's score to a z-score. A) 2 B) -2 C) 18 D) -18 Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than or greater than Round the z-score to the nearest tenth if necessary. 32) A body temperature of 99.7 F given that human body temperatures have a mean of F and a standard deviation of A) 2.4; unusual B) 2.4; not unusual C) -2.4; unusual D) 1.5; not ususal Determine which score corresponds to the higher relative position. 33) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? A) A score of 92 B) A score of 688 C) Both scores have the same relative position. Find the percentile for the data point. 34) Data set: ; data point 51 A) 43 B) 50 C) 57 D) 20 9

10 Find the indicated measure. 35) Use the given sample data to find Q A) 61.0 B) 55.0 C) 67.0 D) 6.0 Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. 36) Construct a boxplot for the data given in the stem-and-leaf plot A) B) C) D) 10

11 Construct a modified boxplot for the data. 37) The weights (in ounces) of 27 tomatoes are listed below. Construct a modified boxplot for the data A) B) C) D) 11