Question
In: Statistics and Probability
If a researcher found that there was a correlation of r = -0.67 between the number...
If a researcher found that there was a correlation of r = -0.67 between the number of siblings a person has and introversion, and the researcher sampled n = 30 people, what conclusions can you make about this relationship
Solutions
Expert Solution
The correlation coefficient is -0.67. Hence it is clear that there is a negative linear relationship between the number of siblings a person has and introversion. The strength of the linear relationship is fairly strong.
Significance test
We will check whether the correlation coefficient is significant or not, say at a 5% level of significance.
The following needs to be tested:
where 
corresponds to the population correlation.
The sample size is n=30, so then the number of degrees of freedom is df=n−2=30−2=28
The corresponding critical correlation value rc for a significance level of α=0.05, for a two-tailed test, is:
Observe that in this case, the null hypothesis H0:ρ=0 is rejected if |∣r∣>rc=0.361.
Based on the sample correlation provided, we have that ∣r∣=0.67>rc=0.361, from which it is concluded that the null hypothesis is rejected and therefore there seems to be a significant correlation between the two variables.
Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!
orchestra answered 11 months agoRelated Solutions
If a researcher found a Person correlation of r = 0.32 between aggression and frequency of...
If a researcher found a Person correlation of r = 0.32 between
aggression and frequency of binge drinking in a sample of n = 52
undergraduate students. Therefore, he can conclude that
__________.
A. there is no significant relationship between these variables
with either, p <.05 and p <.01
B. there is a significant positive relationship between these
variables with p <.05 but not with p <.01.
C. there is a significant positive relationship between these
variables with both, p...
A researcher is interested in determining whether there is a correlation between number of packs of...
A researcher is interested in determining whether there is a
correlation between number of packs of cigarettes smoked
# packs of cigarettes smoked (X)
(Y)
0
80
0
70
1
72
1
70
2
68
2
65
3
69
3
60
4
58
4
55
day and longevity (in years). n=10.
A researcher is interested in determining whether there is a correlation between number of packs of...
A researcher is
interested in determining whether there is a correlation between
number of packs of cigarettes smoked per day and longevity (in
years). n=10.
Longevity
# packs of cigarettes smoked (X)
(Y)
0
80
0
70
1
72
1
70
2
68
2
65
3
69
3
60
4
58
4
55
If a researcher found a significant correlation of .83 between years of education and hours spent...
If a researcher found a significant correlation of .83 between
years of education and hours spent attending Golden State Warriors'
basketball games, what would it mean?
a. People with more education spend more time attending
Warriors' basketball games.
b. People with more education spend less time attending
Warriors' basketball games.
c. People hate Warriors
d. People with less education spend less time attending
Warriors' basketball games.
e. People with less education spend more time attending
Warriors' basketball games.
A study found a high positive correlation (r = .921) between the size of the hospital...
A study found a high positive correlation (r = .921) between the
size of the hospital where a patient's surgery was performed and
the length of the patient's stay following surgery. (x = number of
beds in the hospital, y = number of days following surgery before
release from the hospital). Is the most reasonable explanation for
this correlation cause-and-effect or a hidden cause? If it is not
cause-and-effect, suggest a more reasonable hidden cause.
1)A researcher believes that there is a correlation between the number of cigarettes smoked per day...
1)A researcher believes that there is a correlation between the
number of cigarettes smoked per day and
intelligence. The following data were collected on 15
smokers. Find Pearson's r.
Number of cigarettes (X)
IQ score (Y)
7 10
49 6
41 15
38 5
37 12
19 4
35 19
40 11
1 3
10 3
18 22
21 17
15 12
7 9
38 13
n=15
Sum of X= 376 Sum of
Y=161
Sum...
A researcher conducts a long-term study of the correlation between the number of children a family...
A researcher conducts a long-term study of the correlation
between the number of children a family has (X) and the number of
pets they have 20 years later (Y). He finds the following
results:
Children
(X)
Pets 20 years later (Y)
2
4
4
6
3
1
0
2
1
2
First, the researcher wants to calculate the correlation between
the two variables. Using this dataset, calculate r. (3 pts)
Next, the researcher wants to use his knowledge about...
A positive correlation (r=60) is found between time spent outside at age four and creativity in...
A positive correlation (r=60) is found between time spent
outside at age four and creativity in kindergarten.
Describe what prediction can be made in regards to creativity in
kindergartden for a child who spent a lot of time outside at age
four.
If a journalist made an error in causality when writing an
article about these findings, what would they be concluding based
on this scenario?
If the researcher had a sample size of 13 and started with a
directional...
A correlation of r = +0.7 between gender and height.
Information
For each of Questions 1 to 5, is the given value of the correlation coefficient reasonable?
Hint: think about the strength and the direction of the relationship between the two variables in each case.
Note: It is subjective to decide whether the magnitude of the correlation between two variables should be, for example, 0.7 or 0.8. The below questions don't ask you to make a decision like this.
Question 1
A correlation of r = +0.7 between gender and...
A researcher decides to examine whether there is a correlation between cost of a packet of...
A researcher decides to examine whether there is a correlation
between cost of a packet of chocolate chip cookies (rounded to the
nearest dollar) and degree of customer satisfaction (on a scale of
1 - 10 with a 1 being not at all satisfied and a 10 being extremely
satisfied). A sample of the data is provided below.
Dollars (X)
Satisfaction (Y)
11
6
18
8
17
10
15
4
9
9
5
6
12
3
19
5
22
2...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Engine Cycles a. Write a description of an 'engine cycle'. Use figures, grabs and/or image to...
- orley Company buys surgical supplies from a variety of manufacturers and then resells and delivers these...
- You are creating an enhanced entity relationship model for a campus information system. A junior team...
- The following time series shows the sales of a particular product over the past 12 months....
- Would the voltage of a battery in circuit be larger or smaller than the voltage of...
- The current asset section of the Excalibur Tire Company’s balance sheet consists of cash, marketable securities,...
- Part 1: Explain and provide a real life business example for equivalent units. Explain the importance...
ADVERTISEMENT