Stat 201: Business Statistics I Additional Exercises on Chapter Chapter 3

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1 Stat 201: Business Statistics I Additional Exercises on Chapter Chapter 3 Student Name: Solve the problem. 1) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: Find the median of the observations. Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 2) The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score ) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age ) Six college students spent $215.84, $220.54, $267.63, $214.88, $280.07, and $ respectively for books. Compute the mean amount spent. Round your answer to the nearest cent. 5) Frank's Furniture employees earned the following amounts last week: $ $ $ $ $ $ $ $ $ What was the mean amount earned by an employee last week? Round your answer to the nearest cent. 6) Bill kept track of the number of hours he spent exercising each week. The results for four months are shown below. Find the mean number of hours Bill spent exercising per week

2 Find the median for the given sample data. 7) The salaries of ten randomly selected doctors are shown below. $127,000 $128,000 $180,000 $200,000 $227,000 $108,000 $144,000 $731,000 $249,000 $188,000 Find the median salary. 8) In ten trips to Las Vegas, a person had the following net gains: $3974 $1219 $4716 $6412 $1377 $3690 $6648 $8891 $6509 $4427 Find the median net gain. 9) The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period Find the range for the given data. 10) The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below ) Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filter change at twelve competing service stations Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 12) The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below

3 13) The normal monthly precipitation (in inches) for August is listed for 12 different U.S. cities Solve the problem. 14) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: Company A $70.7 Company F $27 Company B 63 Company G 24.3 Company C 55.9 Company H 23.7 Company D 54.8 Company I 23.9 Company E 30.2 Company J 20.4 Calculate the mean and median for the data. 15) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the 2006 Winter Olympics. Find the mean, median, and mode of the numbers of medals won by these countries ) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spend (in million of dollars) were listed: Company A $72.2 Company F $27.4 Company B 62.9 Company G 25.7 Company C 57.2 Company H 23.2 Company D 55.1 Company I 23.8 Company E 28 Company J 19.5 Calculate the sample variance. 17) The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. 180, 160, 155, 115, 150 3

4 18) The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the 2006 Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries ) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 75 and 3, respectively, and the distribution of scores is mound-shaped and symmetric. Suppose the trainee in question received a score of 71. Compute the trainee's z-score. 20) A radio station claims that the amount of advertising each hour has a mean of 13 minutes and a standard deviation of 1.4 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 9 minutes. Calculate the z-score for this amount of advertising time. 21) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is Find the z-scores for the highest and lowest exam scores. Determine the quartile or interquartile range as specified. 22) The test scores of 15 students are listed below. Find the first quartile, Q ) The test scores of 19 students are listed below. Find the interquartile range

5 24) The weekly salaries (in dollars) of sixteen government workers are listed below. Find the third quartile, Q ) The normal annual precipitation (in inches) is given below for 21 different U.S. cities. Find the first quartile, Q ) The weights (in pounds) of 18 randomly selected adults are given below. Find the third quartile, Q Obtain the five-number summary for the given data. 27) The test scores of 15 students are listed below ) The normal annual precipitation (in inches) is given below for 21 different U.S. cities Construct a boxplot or a modified boxplot as specified. 29) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data set ) The test scores of 40 students are listed below. Construct a boxplot for the data set

6 31) The highest temperatures ever recorded (in F) in 32 different U.S. states are shown below. Construct a boxplot for the data set ) The weights (in ounces) of 27 tomatoes are listed below. Construct a modified boxplot for the data Obtain the population standard deviation, σ, for the given data. Assume that the data represent population data. Round your final answer to one more decimal place than that used for the observations. 33) The weekly salaries (in dollars) of seven government workers are listed below ) The test scores of 9 students are listed below Solve the problem. 35) To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, a researcher divides a field into eight plots of equal size and applies differing amounts of fertilizer to each. The yield of potatoes (in pounds) and the fertilizer application (in pounds) are recorded for each plot. The data are as follows: x y Summary statistics yield SSxx = 10.5, SSyy = 112, SSxy = 25, and SSE = Calculate the coefficient of correlation. Obtain the linear correlation coefficient for the data. Round your answer to three decimal places. 36) x y ) x y

7 38) The data below show the cost of advertising (x), in thousands of dollars, and the number of products sold (y), in thousands, for each of eight randomly selected product lines. x y ) A study was conducted to compare the number of hours spent in the computer lab on an assignment (x) and the grade on the assignment (y), for each of eight randomly selected students in a computer class. The results are recorded in the table below. x y ) Managers rate employees according to job performance (x) and attitude (y). The results for several randomly selected employees are given below. x y Solve the problem. 41) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the number of grunts and and the age of the warthog (in days) are listed below: Number of Grunts Age (days) Find and interpret the value of r. 7

8 42) Consider the following pairs of observations: x y Find and interpret the value of the coefficient of correlation. 43) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the number of grunts and and the age of the warthog (in days) are listed below: Number of Grunts Age (days) Find and interpret the value of r 2. 44) A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. A random sample of seven new salespeople produced the data on experience and sales shown in the table. Months on Job Monthly Sales y ($ thousands) Summary statistics yield SSxx = , SS xy = , SSyy = , x = , and y = Using SSE = , find and interpret the coefficient of determination. 45) Consider the following pairs of observations: x y Find and interpret the value of the coefficient of determination. 8

9 Answer Key Testname: STAT 201 ADDITIONAL EXERCISES ON CHAPTER 3T 1) 74 2) ) 57.9 yr 4) $ ) $ ) 8.03 hr 7) $184,000 8) $ ) 28 10) 5.2 mi 11) $14 12) 7.91 mi 13) 1.05 in. 14) The mean of the data is x = x n = = $39.39 million The median is the average of the middle two observations. M = = $28.60 million 15) The mean is the sum of the numbers divided by 18: = = 13 medals. The median is the mean of the two middle numbers: The mode is the most frequent number of medals: 11 medals. 16) ) ) The range is 29-1 = 28 medals. = 11 medals. The variance is s 2 = x2 - n - 1 x 2 n The standard deviation is s = s2 = 19) z = )z = ) highest: z = 1.51; lowest: z = = (234) =

10 Answer Key Testname: STAT 201 ADDITIONAL EXERCISES ON CHAPTER 3T 22) ) 28 24) $ ) 15.4 in. 26) 173 lb 27) 42, 56, 68, 86, 95 28) 5.1, 14.5, 22.0, 32.7, 51.7 inches 29) 30) 31) 32) 33) $ ) )r = SSxy = SSxx SSyy 25 (10.5)(112) = ) ) ) ) ) ) r =.792; There is a positive linear correlation between age and number of grunts. 42)SSxy = (21)(9.9) 5 SSyy = (9.9) 2 5 = 3.52; SSxx = 99 - (21) 2 5 = 1.188; r = = 10.8; ; There is a strong linear relationship between x and y. 43)r2 =.627; 62.7% of the variation in number of grunts can be explained by using age in a linear model. 10

11 Answer Key Testname: STAT 201 ADDITIONAL EXERCISES ON CHAPTER 3T 44)r2 = SS yy - SSE SSyy = = % of the variation in the sample monthly sales values can be explained by using months on the job in a linear model. 45)SSyy = 1.188; SSE = ; r 2 = ; 96.57% of the sample variation in y values can be attributed to the linear relationship between x and y. 11