Tutorial 1 MTH3003

MTH3003 FIRST SEMESTER 2013/14 TUTORIAL 1 1. Identify each variable as quantitative or qualitative: a. Number of studen...

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MTH3003 FIRST SEMESTER 2013/14

TUTORIAL 1 1. Identify each variable as quantitative or qualitative: a. Number of students in first-grade classroom b. Amount of time it takes to assemble a simple puzzle c. State in which a person live d. Ethnic origin a of candidate for public office e. Mercury concentration in a sample of tuna

2. Identify the following quantitative variables as discrete or continuous a. Population in a particular area of United States b. Time to complete a sociology exam c. Weight of newspapers recovered for recycling on a single day d. Time required to complete a questionnaire e. Number of defective light bulbs in a package containing four bulbs

3. Six vehicles are selected from the vehicles that are issued campus parking permits, and the following data are recorded: Vehicle

Types

Make

Carpool?

1 2 3 4 5 6

Car Car Truck Van Motorcycle Van

Honda Toyota Toyota Dodge Harley Davidson Chevrolet

No No No Yes No No

One-way Commute Distance (miles) 23.6 17.2 10.1 31.7 25.5 5.4

Age of vehicle (year) 6 3 4 2 1 9

a. What are the experimental units? b. What are the variable being measured? What types of variables are they? c. Is this univariate, bivariate, or multivariate data?

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4. A manufacturer of jeans has plants in California, Arizona, and Texas. A group of 25 pairs of jeans is randomly selected from the computerized database, and the state in which is produced is recorded:

CA CA AZ CA CA

AZ CA AZ AZ AZ

AZ TX CA TX AZ

TX TA AZ TX CA

CA TX TX TX CA

a. What is the experimental unit? b. What is the variable being measured? Is it qualitative or quantitative? c. Construct a pie chart to describe the data. d. Construct a bar chart to describe the data. e. What proportions of the jeans are made in Texas? f.

What state produced the most jeans in the group?

g. If you want to find out whether the three plants produced equal number of jeans, or whether one produced more jeans than the others, how can you use the charts from part c and d to help you? What conclusion can you draw from these data?

5. The ages (in months) at with 50 children were first enrolled in a preschool are listed below. 38 47 32 55 42

40 35 34 39 50

30 34 41 33 37

35 43 30 32 39

39 41 46 32 33

40 36 35 45 45

48 41 40 42 38

36 43 30 41 46

31 48 46 46 46

36 40 37 51 31

a. Construct a stem and leaf display for the data. b. Construct a relative frequency histogram for these data. Start the lower boundary of the first class at 30 and use a class width of 5 months. c. Compare the graphs in parts a and b. are there any significant differences that would cause you to choose one of the better method for displaying the data? d. What proportion of the children were 35 months (2 years, 11 months) or older, but less than 45 months (3 years, 9 months) of age when first enrolled in preschool?

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6. The number of calories per serving for selected ready-to-eat cereals is listed below. 130 190 140 80 100 120 220 210 130 100 90 210 120 200 190 210 120 200 130 180 260 190 240 80 120 90 190 200 115 210 110 225 190 130 a. Construct a frequency distribution using 7 classes.

220 120 270 210

110 10 100 190

100 120 160 180

b. Draw a relative frequencies histogram for this data. Use the smallest value in the data set as lower class limit. c. Find the mean and modal class. d. Describe the shape of histogram.

7. You are given n = 8 measurements; 3, 2, 5, 6, 4, 4, 3, 5. a. Find the mean, median, and mode. b. Based on result in of mean and median, are the measurements symmetric or skewed? Draw a dotplot to confirm your answer. 8. The article in Consumer Reports gives the price – an estimated average for 6-ounce can or a 7.06 –ounce pouch – for 14 different brands of water – packed light tuna, based on priced paid nationally in supermarkets. 0.99

1.92

1.23

0.85

0.65

0.53

1.41

1.12

0.63

0.67

0.69

0.60

0.60

0.66

a. Find the average price for the 14 different brands of tuna. b. Find the median price for the 14 different brands of tuna. c. Based on your findings in part a and b, do you think that the distribution of prices is skewed? Explain.

9. You are given n = 8 measurements; 3, 1, 5, 6, 4, 4, 3, 5. a. Calculate the range and sample mean. b. Calculate the sample variance and standard deviation. c. Compare the range and the standard deviation. The range is approximately how many standard deviations?

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10. The data listed here are the weights (in pounds) of 27 packages of ground beef in supermarket meat display: 1.08 1.06

0.99 1.14

0.97 1.38

1.18 0.75

1.28 1.08

0.83 0.87

0.89 0.89

0.89 0.98

0.96 1.14

1.12 1.18

0.93 1.17

1.24

a. Find the mean and standard deviation of the data set. b. Find the percentage measurements in the intervals, x

s , x 2s and x 3s .

c. How do the percentages obtained in part c compare with those given by the Empirical Rule? Explain. d. How many of the packages weigh exactly 1 pound? Can you think of any explanation for this?

11. Given the following data set: 8, 7, 1, 4, 6, 6, 4, 5, 7, 6, 3, 0 a. Find the five-number summary and the IQR. b. Calculate

and

c. Calculate the

-score for the smallest and largest observations. Is either of these

observations unusually large or unusually small?

12. The number of raisins in each of 14 mini boxes (1/2-ounce size) was counted for a generic brand and for Sunmaid brand raisins. The two of data sets are shown here:

Generic Brand 25 26 24 26 28 28 26 27 27 26 26 25 25 28

25 28 25 28 22

Sunmaid 29 24 28 24 27

24 28 30 24

a. What are the mean and standard deviation for the generic brand? b. What are the mean and standard deviation for the Sunmaid brand? c. Compare the centers and variabilities of the two brands using the results of part a and b. d. Find the median, the upper and lower quartiles, and the IQR for each of the two data sets.

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e. Construct two box plots on the same horizontal scale to compare the two sets of data. f.

Draw two stem and leaf plots to depict the shapes of the two data sets. Do the box plots in part e verify the results?

References: - Mendenhall, W., Beaver, R. J. & Beaver, B. M. (2009). Introduction to Probability and Statistics. 13th ed. - Bluman, Allan G. 2004. Elementary Statistics: A Step by Step Approach. 5th ed.

Q1 :

Exc. 1.3 - 1.2-a,b,d (pg 14) Supplementary Exc. – 1.38-a,d (pg 43)

Q2:

Ex. 1.3 – 1.3-a,b,c (pg 15) Supplementary Ex. – 1.40-d,e (pg 43)

Q3:

Ex. 1.3 – 1.5 (pg 15)

Q4:

Ex. 1.3 – 1.11 (pg 16)

Q5:

Ex. 1.5 – 1.28 (pg 31)

Q6:

Bluman, Allan G. 2004. Elementary Statistics: A Step by Step Approach. 5th ed.

Q7:

Ex. 2.2 – 2.2 (pg 58)

Q8:

Ex. 2.2 – 2.8 (pg 59)

Q9:

Ex. 2.3 – 2.16 (pg 65)

Q10:

Ex. 2.5 – 2.24 (pg72)

Q11:

Ex. 2.7 – 2.42 (pg 84)

Q12:

Supplementary Ex. – 2.54, 2.55 (pg 90) 5