Question
In: Statistics and Probability
We surveyed 10 people all in their 20s, asking them the number of books they have...
We surveyed 10 people all in their 20s, asking them the number of books they have read this year.
| Age (x) | Number of Books Read This Year (y) |
| 20 | 5 |
| 21 | 2 |
| 22 | 1 |
| 23 | 6 |
| 24 | 0 |
| 25 | 10 |
| 26 | 8 |
| 27 | 1 |
| 28 | 2 |
| 29 | 1 |
a). Calculate the mean, median, and standard deviation
b). Estimate a regression equation for the two variables
Solutions
Expert Solution
a )
| x (1) |
Frequency (f) (2) |
f⋅x (3)=(2)×(1) |
f⋅x2=(f⋅x)×(x) (4)=(3)×(1) |
cf (5) |
| 20 | 5 | 100 | 2000 | 5 |
| 21 | 2 | 42 | 882 | 7 |
| 22 | 1 | 22 | 484 | 8 |
| 23 | 6 | 138 | 3174 | 14 |
| 24 | 0 | 0 | 0 | 14 |
| 25 | 10 | 250 | 6250 | 24 |
| 26 | 8 | 208 | 5408 | 32 |
| 27 | 1 | 27 | 729 | 33 |
| 28 | 2 | 56 | 1568 | 35 |
| 29 | 1 | 29 | 841 | 36 |
| --- | --- | --- | --- | --- |
| n=36 | ∑f⋅x=872 | ∑f⋅x2=21336 | -- |
Mean ˉx=∑fx/n
=872/36
=24.2222
Median :
M = value of (n/2)th observation
= value of (36/2)th observation
= value of 18th observation
From the column of cumulative frequency cf, we find that the 18th
observation is 25.
Hence, the median of the data is 25.
Standard deviation = 
= 
= 
= 2.4394
b ) Sum of X = 245
Sum of Y = 36
Mean X = 24.5
Mean Y = 3.6
Sum of squares (SSX) = 82.5
Sum of products (SP) = -10
Regression Equation = ŷ = bX + a
b = SP/SSX = -10/82.5 =
-0.12121
a = MY - bMX = 3.6 -
(-0.12*24.5) = 6.5697
ŷ = -0.12121X + 6.5697
orchestra answered 2 years agoRelated Solutions
A researcher surveyed randomly selected Democrats and Republicans asking them what the number one concern should...
A researcher surveyed randomly selected Democrats and
Republicans asking them what the number one concern should be for
the president of the United States. The results of the survey are
shown below. Is there evidence to conclude that there is a
difference in what Democrats and Republicans think is the most
important?
Frequencies of Concerns for Democrats and
Republicans
Economy
Foreign Affairs
Family Values
Environment
Other
Democrats
83
47
81
85
50
Republicans
84
64
94
53
35
What can...
A researcher surveyed randomly selected Democrats and Republicans asking them what the number one concern should...
A researcher surveyed randomly selected Democrats and
Republicans asking them what the number one concern should be for
the president of the United States. The results of the survey are
shown below. Is there evidence to conclude that there is a
difference in what Democrats and Republicans think is the most
important?
Frequencies of Concerns for Democrats and
Republicans
Economy
Foreign
Affairs
Family
Values
Environment
Other
Democrats
88
55
83
70
32
Republicans
114
71
120
40
36
What can...
A pollster surveyed a sample of 980 adult Americans, asking them if they own a personal...
A pollster surveyed a sample of 980 adult Americans, asking them
if they own a personal firearm. 34% of the sample said yes.
1. What is a 90% confidence interval estimate for the percentage
of Americans that own a firearm?
2. A gun owners’ group claims that more Americans own a firearm
in 2015 than ten years ago, when the percentage of owners was 30%.
At the 0.05 level of significance, has the percentage of owners
increased?
3. What is...
A probability and statistics professor surveyed 11 students in her class, asking them questions about their...
A probability and statistics professor surveyed 11 students in
her class, asking them questions about their study strategy. The
number of hours studied and the grade for the course test are in
the table below:
Hours Studied (X)
11
99
22
44
99
11
88
1010
66
99
22
Test Grade (Y)
46
91
57
71
90
52
81
98
82
94
64
1.The correlation coefficient is....
he correlation coefficient in part a. suggests that the
relationship between Hours Studied...
Suppose you have surveyed thirty people and asked them whether they are white (W) or nonwhite...
Suppose you have surveyed thirty people and asked them whether
they are white (W) or nonwhite (N), and how many traumas (serious
accidents, rapes, or crimes) they have experienced in the past
year. You also asked them to tell you whether they perceive
themselves as being in the upper, middle, working, or lower class.
Your survey resulted in the following raw data:
Race
Age
(years)
Class
Traumas (#)
W
18
W
0
W
45
M
2
W
23
W
1...
ou've surveyed all of the instructors in the CRMJ department at WSU asking what their current...
ou've surveyed all of the instructors in the CRMJ department at
WSU asking what their current research interests are. They fall
into these three categories: policing, corrections, courts. You
want to know if the gender of the instructor affects their research
interest. Of the women in the department, 10 are researching
police, 8 are researching corrections, and 15 are researching
courts. Of the men in the department, 16 are researching police, 10
are researching corrections, and 6 are researching courts....
6. There are 40 books on a bookshelf. Exactly 10 of them have a red cover....
6. There are 40 books on a bookshelf. Exactly 10 of them have a
red cover. The remaining books have a white cover. You intend to
choose a random sample of nine books, but you haven't decided
whether to choose with replacement or without replacement?
a) If you choose books with our placement, would this procedure
lead to independent trials or dependent trials?
b)if you choose books with replacement, would this procedure be
consistent with a binomial experiment or not?...
In chapter 12 we discussed Stereotypes, Prejudice and Discrimination. We all have them, and acknowledging them...
In chapter 12 we discussed Stereotypes, Prejudice and
Discrimination. We all have them, and acknowledging them is
important, and often uncomfortable. For your final Reaction paper,
I would like you to think about a specific stereotype or prejudice
you hold. Discuss your stereotype or prejudice and reflect on it,
explaining where it came from, what reinforcements you've received
in regard to it and how it has affected your behavior.
link for the text book to log in to chapter 12...
There are 4 people in a room, and we are curious whether two of them have...
There are 4 people in a room, and we are curious whether two of
them have their birthday in the same month. We record the quadruple
that describes the month of birthday for each person. E.g. (Oct,
Jan, Jul, Apr) is one possible quadruple /outcome.(Since each month
applies to a specific person, (Oct, Jan, Jul, Apr) is not the same
as(Jan, Jul, Oct, Apr) and so order is important.)
a.How many possible outcomes are there?
b.In how many of these...
A pollster surveys people at a boxing match, asking them if they had even struck their...
A pollster surveys people at a boxing match, asking them if they
had even struck their spouse. Of the 32 people surveyed, 30 said no
and the other 2 did not respond. What type of bias is in this
sample?
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Make-or-Buy Decision Fremont Computer Company has been purchasing carrying cases for its portable computers at a...
- The following costs were incurred for the single product produced during the first year of operations...
- Non-constant growth model: Do=$2.00 required return on equity= 5% g= 9% n=1,2 g=7% n=3,4 g=3% n=5...
- . Find all x ∈ Z143 such that x2Ξ 7 (mod 143). Please explain all steps...
- #Python: A palindrome is a sequence of characters that reads the same backwards as forwards. For...
- Explain an example in which a variable has two different addresses at different places in a...
- Hadley, a thirty-five-year-old physician, has worked at Princeton Plainsboro Hospital for six years. She recently received...
ADVERTISEMENT