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 3 years ago
Next > < Previous

Related 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...
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...
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...
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
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT