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- 1 To estimate the average number of minutes

1. To estimate the average number of minutes it takes a typical employee at H&R Block to prepare a tax return for a customer, a random sample of 30 employees was selected during last tax season and studied. For each employee in the sample, the total number of minutes to complete a tax return was recorded. The following times resulted: (13 points)
40 48 52 55 59 64 42 50 52 56 61 64 45 50 53 57 62 67 47 51 54 57 62 68 48 51 55 57 63 71
a) Calculate the mean time taken to prepare a tax return for the sample. (4 points)
b) Calculate the standard deviation for the times taken to prepare a tax return in this sample. Interpret the meaning of the standard deviation for this problem. (6 points)
c) Compute the variance for the times taken to prepare a tax return. (3 points)
2. The raw data from the previous question have been summarized in the following grouped frequency distribution: (17 points)
Number of Minutes to Prepare a Tax Return, xNumber of Employees, f
40 44 2
45 49 4
50 54 8
55 59 7
60 64 6
65 69 2
70 74 1
a) Find the mean time taken to prepare a tax return for the 30 employees from the grouped frequency distribution. Explain or show how you arrived at your answer. (Use extra columns in the table if needed.) (6 points)
b) What is the modal class? (4 points)
c) What is the median class? (4 points)
d) Why is the mean you calculated in part a) of this question an estimate? (3 points)
3. Suppose there are ten employees at a small company. Suppose you are told that µ = 40.5 and you are given nine of the ten employees ages. The data is as follows: (8 points)
22 68 40 4839 38 20 60 39_?_
a) What is the missing data value? (4 points)
b) What symbol would you use to denote the standard deviation of this data?
i) S or ii) Æ (select one) (4 points)
4. The following table summarizes the number of cases of each type of operation performed at General Hospital last year. (8 points)
Type of Operation Number of Cases
Thoracic 20
Bones and Joints 45
Eye, ear, nose and throat 58
General 98
Abdominal 115
Urologic 74
Proctologic 65
Neurosurgery 23
a) Which measure of central tendency (the mean, the median, or the mode) is the most appropriate one to choose if you want to summarize the "average" for the above data? (4 points)
b) What is the "average" type of operation performed at General Hospital? (4 points)
5. Suppose a company advertises that the mean weight loss after using the Techno-fit Ultra, (its brand new fitness machine), four times per week for two months is 15 pounds. The company came to this conclusion by carefully monitoring 20 participants who used the machine four times per week for two months. At the end of two months, the weight loss (in pounds) was recorded. The data that resulted have been summarized in the stem-and-leaf display below. (19 points)
Weight Loss Using the Techno-fit Ultra
0| 0 2 3 5 5 7 7 7 7 8
1|1 2 3 4 5 8 9
2|6
3|
4|5
5|
6|
7|6key: 2|6 = 26 pounds
a) What is the median weight loss for the 20 participants? (4 points)
b) What is the mode for this sample? (4 points)
c) What percent of the participants in the study lost more than the mean number of pounds reported? (4 points)
d) Describe the distribution of weight losses based upon the sample data. Identify any unusual or distinctive features, including the shape of the distribution. (3 points)
e) Assume you are a customer trying to decide whether or not to buy the fitness machine. Did the company report the most representative "average" weight loss? Explain completely and use the shape of the distribution to support your answer. (4 points)
6. The following data represent the number of potholes on ten randomly selected 1-mile stretches for each of two major highways in a nearby city. (15 points)
Highway A: 3212455334
Highway B: 331133 13113
a) Complete the following to summarize the data obtained from highway A. (6 points)
b) Complete the following to summarize the data obtained from highway B. (6 points)
c) Which highway would you prefer to travel? Why? (3 points)

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