Stat 321 - HW 1
Due beginning of class, Tuesday, Jan. 15
1) This activity asks you to consider the value of statistics ratings that you and your classmates gave to Statistics in the Stat 321 Initial survey (1=completely useless to 9=extremely important). The responses of the first 31 individuals were: 6, 9, 9, 6, 7, 9, 7, 7, 7, 9, 9, 7, 7, 7, 7, 7, 6 ,6 ,8, 6, 6, 5, 7, 7, 6, 9, 7, 8, 9, 8, 8
a) Tally
the responses of students in your class by counting how many students answered
1, how many answered 2, and so on. Create a table similar to the following to
organize the data:
|
Rating |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Tally
(count) |
|
|
|
|
|
|
|
|
|
b) Which value was chosen most often
(the “mode”)?
c) How many and what proportion of
students gave a response (strictly) greater than 5? Less than 5?
d) Based on these data, write a paragraph interpreting how your class generally seems to feel about the value of statistics in society. Specifically, comment on the degree to which these students seem to be in agreement. Also address if students seem to be generally optimistic, pessimistic, or undecided about the value of statistics.
e) Suggest a measurement issue that may lead to these responses not being an accurate reflection of the opinions about statistics of the students in this class.
f) Suggest a sampling issue that may explain why these responses are not representative of the opinions of all
Cal Poly students.
2) Reconsider the previous
problem. Examine the following frequency (tally) table for hypothetical classes
A–E. (Consider all empty cells counts of zero.) For each of the following descriptions,
identify which of the classes fits the description best. Hint: Use each class letter once and only once.
|
Rating |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Class A Count |
1 |
4 |
7 |
1 |
|
1 |
3 |
5 |
2 |
|
Class B Count |
2 |
3 |
6 |
5 |
2 |
1 |
2 |
3 |
|
|
Class C Count |
|
|
|
|
|
1 |
19 |
4 |
|
|
Class D Count |
|
2 |
3 |
|
2 |
5 |
6 |
2 |
4 |
|
Class E Count |
2 |
3 |
1 |
3 |
2 |
4 |
5 |
1 |
3 |
i. The class is in considerable agreement
that statistics is useful.
ii. The
class feels generally that statistics is useful but to varying degrees and with
a few disagreements.
iii. The
class displays a wide range of opinions, with a slight preference toward
feeling that statistics is useful.
iv. The
class is sharply divided on the issue.
v. The
class feels generally that statistics is not useful but displays a range of
opinions.
3) A group of undergraduate students
at Cal Poly (Mintz, Mintz, Moore, and Schuh, 2002) conducted a study examining how
much weight students carry in their backpacks. They weighed the backpacks of
100 students and compared the distributions of backpack weights between men and
women.
(a) Compare and contrast the distribution of backpack weights between men and women. (Be sure to discuss each of shape, center, spread, and unusual observations and to put your comments in context.)
(b) Does one sex tend to carry more weight in their backpacks than the other sex? Explain how you can tell from the dotplots.
(c) Suggest another way of looking at backpack weights (a different type of measurement or variable they could have recorded) that might make for more meaningful comparisons.
3) Exercise 36 (p. 30)
4) Exercise 55 (p. 40)
5) Exercise 71 (p. 42)
6) The following
histograms show the distributions of 16 quiz scores for each of four
hypothetical students (named A, B, C, and D):
(a) Without performing any
calculations, arrange these students in order from smallest standard deviation
to largest standard deviation. Explain the reasoning behind your choices.
(b) Determine the value of the
smallest standard deviation among these four students’ quiz scores. Show your
work or explain your answer.
(c) Determine the value of the largest
standard deviation among these four students’ quiz scores. Show your work in
calculating this value by hand.