SOLUTION: GRAPHICAL ANALYSIS OF DATA 1. The list below shows the ages of the first 20 fans to arrive at a professional basketball game. 38, 39, 14, 46, 9, 25, 27, 33, 60, 11, 14, 37,

Question 1140819: GRAPHICAL ANALYSIS OF DATA
1. The list below shows the ages of the first 20 fans to arrive at a professional basketball game.
38, 39, 14, 46, 9, 25, 27, 33, 60, 11, 14, 37, 25, 28, 16, 30, 42, 35, 35, 47
Part A: Display the fan age data on this stem-and-leaf plot. (1 point)

Part B: Use your plot from Part A to display the data in this frequency table. (1 point)

Part C: Use your table from Part B to display the data on this histogram. (1 point)

Part D: Use your results from Parts A - C to answer these questions. (6 points)
What does it mean that the fan data are numerical and univariate?

Are the data discrete or continuous? Explain.

Which age group had the most fans? Explain how to find the answer using each of the three data displays.

Write a question that can be answered using the stem-and-leaf plot but cannot be answered using the frequency table or histogram.

MEASURE AND DESCRIBE DATA
2. Jason is the captain of his basketball team. The list below shows how many points Jason scored in each of the first 10 games of the season.
18, 23, 14, 26, 16, 10, 12, 24, 14, 13
Part A: Find the range, mean, median, and mode of Jason's scores. Show your work. (4 points)

Part B: Use your mean result from Part A to find the variance and standard deviation of Jason's scores. Show your work. Round your answers to the nearest hundredth. (2 points)

Part C: Are your results in Part B for a sample or a population? Explain. (1 point)

Part D: Use your results from Parts A - C to describe the shape of the distribution of Jason's scores. (1 point)

Part E: Use your results from Parts A - D to answer these questions. (3 points)
If Jason scored 40 points on his next game, would it be an outlier for his first 11 games? Explain.
How would a score of 40 affect the range, mean, median, and mode of Jason's scored points?

If Jason could add 10 points to the number of points he scored each game, how would it affect the mean, median, and standard deviation of his scored points?

If Jason could double every game's scored points, how would it affect the mean, median, and standard deviation of his scored points?

RANDOM VARIABLES
3. The table below shows the probabilities of rolling sums from 2 to 12 with a pair of 6-sided dice. Use the table to find the mean of the random variable x (the expected value of the sum rolled with 2 dice).
x
2
3
4
5
6
7
8
9
10
11
12
P(x)

Part A: Complete the table below. You do not need to reduce fractions. The first row is filled in for you. (5 points)
i
xi
P(xi)
xiP(xi)
1
2
1/36
2/36
2
3
2/36

3
4
3/36

4
5
4/36

5
6
5/36

6
7
6/36

7
8
5/36

8
9
4/36

9
10
3/36

10
11
2/36

11
12
1/36

Part B: Find the mean of the random variable x. Use this formula: .(3 points)

EXPERIMENTAL DESIGN
4. Below is a list of 30 students numbered from 00 to 29. Use the random number table below to put exactly 6 of these students into a treatment group. Start with the first line of the table (line 101). List the students of the treatment group in the order in which their numbers come up in the table.
00 Aaron
01 Buffy
02 Chandler
03 Cindy
04 Drusilla
05 Eric
06 Fallon
07 Graham
08 Heather
09 Hsin-Chi
10 Ismail
11 Jasmine
12 Kiefer
13 Lucia
14 Monte
15 Naomi
16 Otis
17 Polly
18 Quincy
19 Rachael
20 Sarah
21 Stacy
22 Tasha
23 Turan
24 Ukiah
25 Valerie
26 Wahib
27 Xandra
28 Yale
29 Zach
Part A: Search through the list for pairs that match student numbers and circle each one found. If a student number is repeated, only use the first occurrence. Stop when you have 6 matches. (3 points)

Part B: List the 6 matching student numbers you found. (3 points)

Part C: Which 6 students will be in the treatment group? (3 points)

REPORTS and EXPERIMENTS
5. Devon wants to know if drinking milk before bed helps teenagers sleep. He chooses 10 friends on his high school basketball team for his study. Every night for one month, the friends drink a glass of milk before bed and later record how many hours they slept that night.

Part A: Describe three reasons why Devon's study design is flawed. (3 points)

Part B: After one month, Devon finds that his 10 friends slept an average of 0.5 hour more each night when they drank milk before bed. Based on this, Devon concludes that drinking milk makes teenagers sleepy. What is one reason why Devon's conclusion is most likely invalid? (1 point)

Part C: A study conducted by a major milk manufacturer showed that 83% of American teenagers prefer drinking milk to drinking soda. What are two reasons why this statistic cannot be trusted? (2 points)

6. A lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. He has 100 mice available. He randomly assigns 50 of them into each group. He trains the first group to run the maze at 9:00 am and trains the second group to run the maze at 9:00 pm. Each mouse is trained the same way and the last three run times are recorded.
Part A: Describe what is being measured in this experiment and what variable is being manipulated. (1 point)

Part B: Control, randomization, and replication are ways to design an experiment so that bias is reduced. Describe whether or not this experiment incorporates each of these principles into the experimental design. (6 points)
Control

Randomization

Replication

Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
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