Problem #1 A physician claims that an experimental medication increases an individual's heart rate. Twelve test subjects are randomly selected and the heart rate of each is measured. The subjects are then injected with the medication and, after one hour, the heart rate of each is measured again. The results are listed below. Assuming the heart rates are normally distributed, is there enough evidence to support the physician's claim at a = 0.05? Before 72 81 76 After 73 80 79 74 75 81 68 76 76 82 74 75 77 78 76 75 75 74 76 77 80
Problem #1 A physician claims that an experimental medication increases an individual's heart rate. Twelve test subjects are randomly selected and the heart rate of each is measured. The subjects are then injected with the medication and, after one hour, the heart rate of each is measured again. The results are listed below. Assuming the heart rates are normally distributed, is there enough evidence to support the physician's claim at a = 0.05? Before 72 81 76 After 73 80 79 74 75 81 68 76 76 82 74 75 77 78 76 75 75 74 76 77 80
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
Related questions
Question
Here’s an example, and here is the problem. Try to solve it as best posible and make sure to label each step with its corresponding number.
![HYPOTHESIS TESTING FOR A POPULATION CORRELATION COEFFICIENT
Remember your symbols:
r=
Sample correlation
Coefficient
Hypotheses, Degrees of Freedom, and the Test Statistic
Hypotheses: While you CAN use left, right, and two-tailed hypotheses for the population.
correlation coefficient, we will ONLY consider two-tailed hypothesis tests for p.
Degrees of Freedom: A t-test will be used to test whether the correlation between two
variables is significant. The degrees of freedom for hypothesis testing for the population
correlation coefficient will be d.f. = n-2 (where n is the number of pairs of data)
Test Statistic: We use the test statistic r (the sample correlation coefficient)
Advertising
expenses
(1000s of $)
USE THE TI-84 LinRegTTest to find your t-test statistic and your p-value
Complete the following steps. Identify each step with the appropriate corresponding number.
1. Write the claim and the null and the alternate hypotheses. 2. Identify a. 3. Draw a
distribution to represent it and identify the critical value(s). 4. Write the inequality that
identifies the rejection area(s). 5. Find the test statistic. 6. Make a decision about your test. 7.
Write a sentence describing your decision about the claim in context with the problem.
2.4
1.6
2.0
2.6
1.4
1.6
2.0
2.2
EXAMPLE 1
Is there enough evidence at a = 0.01 to conclude that there is a significant statistical correlation
between advertising hours and company sales?
Company Sales
(1000s of $)
p= population correlation
225
184
220
240
180
184
186
215
3
41 Ryect Ho if + test
5
Coefficent
Claim There is a statistical
Correlation between advertising
hours and company sales.
Ho: P = O
H₁: P =
3,707 or t-test ≤-3707
r=01913
t=5,478
P-value 0.00155
6 Ryect. Ho
IN
t=-3707
m
+=3,707
There is evidence at
a =, 01 to support the claim
that there is a significent
Correlation between
advertising sales
and company sales.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1111448-eb79-4dcb-9c63-e4c0efd60223%2Fe5018f6d-6c52-4898-a596-695c053e39d6%2F1fdabq7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:HYPOTHESIS TESTING FOR A POPULATION CORRELATION COEFFICIENT
Remember your symbols:
r=
Sample correlation
Coefficient
Hypotheses, Degrees of Freedom, and the Test Statistic
Hypotheses: While you CAN use left, right, and two-tailed hypotheses for the population.
correlation coefficient, we will ONLY consider two-tailed hypothesis tests for p.
Degrees of Freedom: A t-test will be used to test whether the correlation between two
variables is significant. The degrees of freedom for hypothesis testing for the population
correlation coefficient will be d.f. = n-2 (where n is the number of pairs of data)
Test Statistic: We use the test statistic r (the sample correlation coefficient)
Advertising
expenses
(1000s of $)
USE THE TI-84 LinRegTTest to find your t-test statistic and your p-value
Complete the following steps. Identify each step with the appropriate corresponding number.
1. Write the claim and the null and the alternate hypotheses. 2. Identify a. 3. Draw a
distribution to represent it and identify the critical value(s). 4. Write the inequality that
identifies the rejection area(s). 5. Find the test statistic. 6. Make a decision about your test. 7.
Write a sentence describing your decision about the claim in context with the problem.
2.4
1.6
2.0
2.6
1.4
1.6
2.0
2.2
EXAMPLE 1
Is there enough evidence at a = 0.01 to conclude that there is a significant statistical correlation
between advertising hours and company sales?
Company Sales
(1000s of $)
p= population correlation
225
184
220
240
180
184
186
215
3
41 Ryect Ho if + test
5
Coefficent
Claim There is a statistical
Correlation between advertising
hours and company sales.
Ho: P = O
H₁: P =
3,707 or t-test ≤-3707
r=01913
t=5,478
P-value 0.00155
6 Ryect. Ho
IN
t=-3707
m
+=3,707
There is evidence at
a =, 01 to support the claim
that there is a significent
Correlation between
advertising sales
and company sales.
![NAME
**For each of the following, complete the steps listed below. Identify and write each step
with the appropriate corresponding number. 1. Write the claim and the null and the
alternate hypotheses with proper notation. 2. Identify the level of significance. 3. Draw
a distribution to represent it and identify the critical value. 4. Write the inequality that
identifies the rejection area(s). 5. USE YOUR CALCULATOR to find the t-test statistic
and the p-value. 6. Make a decision about your test. 7. Write a sentence describing your
decision about the claim.
Problem #1
A physician claims that an experimental medication increases an individual's heart rate.
Twelve test subjects are randomly selected and the heart rate of each is measured. The
subjects are then injected with the medication and, after one hour, the heart rate of each
is measured again. The results are listed below. Assuming the heart rates are normally
distributed, is there enough evidence to support the physician's claim at a = 0.05?
Before 72 81 76 74
After 73 80 79 76
75
76
81 68 75
82 74 77
78 76 74
75 75 76
77
80](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1111448-eb79-4dcb-9c63-e4c0efd60223%2Fe5018f6d-6c52-4898-a596-695c053e39d6%2Fh9utnu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:NAME
**For each of the following, complete the steps listed below. Identify and write each step
with the appropriate corresponding number. 1. Write the claim and the null and the
alternate hypotheses with proper notation. 2. Identify the level of significance. 3. Draw
a distribution to represent it and identify the critical value. 4. Write the inequality that
identifies the rejection area(s). 5. USE YOUR CALCULATOR to find the t-test statistic
and the p-value. 6. Make a decision about your test. 7. Write a sentence describing your
decision about the claim.
Problem #1
A physician claims that an experimental medication increases an individual's heart rate.
Twelve test subjects are randomly selected and the heart rate of each is measured. The
subjects are then injected with the medication and, after one hour, the heart rate of each
is measured again. The results are listed below. Assuming the heart rates are normally
distributed, is there enough evidence to support the physician's claim at a = 0.05?
Before 72 81 76 74
After 73 80 79 76
75
76
81 68 75
82 74 77
78 76 74
75 75 76
77
80
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