A research article describes a study that investigated the relationship between depression and chocolate consumption. Participants in the study were 931 adults who were not currently taking medication for depression. These participants were screened for depression using a widely used screening test. The participants were then divided into two samples based on the score on the screening test. One sample consisted of people who screened positive for depression, and the other sample consisted of people who did not screen positive for depression. Each of the study participants also completed a food frequency survey. The researchers believed that the two samples were representative of the two populations of interest-adults who would screen positive for depression and adults who would not screen positive. The paper reported that the mean number of servings of chocolate for the sample of people that screened positive for depression was 8.44 servings per month, and the sample standard deviation was 14.82. For the sample of people who did not screen positive for depression, the mean number of servings per month was 5.29, and the standard deviation was 8.78. The paper did not say how many individuals were in each sample, but for the purposes of this exercise, you can assume that the 931 study participants were divided into 311 who screened positive for depression and 620 who did not screen positive. Carry out a hypothesis test to confirm the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater than the mean number of chocolate servings per month for people who would not screen positive for depression. (Use α = 0.05. Use μ₁ for people who would screen positive for depression and μ₂ for people who would not screen positive.) State the appropriate null and alternative hypotheses. HH-0 Mai My-M₂-0 Ho: H1-20 Ha H₁₂ = 0 Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value=

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
icon
Related questions
Question

11.1.4

State the conclusion in the problem context.
○ We fail to reject Ho. The test does not confirm the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for
depression is greater than the mean number of chocolate servings per month for people who would not screen positive.
We reject Ho. The test does not confirm the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is
greater than the mean number of chocolate servings per month for people who would not screen positive.
We reject Ho. The test confirms the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater
than the mean number of chocolate servings per month for people who would not screen positive.
We fail to reject Ho- The test confirms the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is
greater than the mean number of chocolate servings per month for people who would not screen positive.
You may need to use the appropriate table in the appendix or technology to answer this question.
Transcribed Image Text:State the conclusion in the problem context. ○ We fail to reject Ho. The test does not confirm the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater than the mean number of chocolate servings per month for people who would not screen positive. We reject Ho. The test does not confirm the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater than the mean number of chocolate servings per month for people who would not screen positive. We reject Ho. The test confirms the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater than the mean number of chocolate servings per month for people who would not screen positive. We fail to reject Ho- The test confirms the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater than the mean number of chocolate servings per month for people who would not screen positive. You may need to use the appropriate table in the appendix or technology to answer this question.
A research article describes a study that investigated the relationship between depression and chocolate consumption. Participants in the study were 931 adults who were not currently
taking medication for depression. These participants were screened for depression using a widely used screening test. The participants were then divided into two samples based on the
score on the screening test. One sample consisted of people who screened positive for depression, and the other sample consisted of people who did not screen positive for depression.
Each of the study participants also completed a food frequency survey.
The researchers believed that the two samples were representative of the two populations of interest-adults who would screen positive for depression and adults who would not screen
positive. The paper reported that the mean number of servings of chocolate for the sample of people that screened positive for depression was 8.44 servings per month, and the sample
standard deviation was 14.82. For the sample of people who did not screen positive for depression, the mean number of servings per month was 5.29, and the standard deviation was
8.78. The paper did not say how many individuals were in each sample, but for the purposes of this exercise, you can assume that the 931 study participants were divided into 311 who
screened positive for depression and 620 who did not screen positive.
Carry out a hypothesis test to confirm the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater
than the mean number of chocolate servings per month for people who would not screen positive for depression. (Use α = 0.05. Use μ₁ for people who would screen positive for
depression and μ for people who would not screen positive.)
State the appropriate null and alternative hypotheses.
Ho: M₁ - M₂ < 0
Ha M₁ - M₂ > 0
O Ho H1 H2 = 0
-
Ha H1 H20
O Ho H1-H2=0
Ha: μ₁ - μ2 % 0
○ Ho: H1 - μ₂ > 0
Ha M₁ - M₂ = 0
O Ho: H₁₂ 0
Ha M1-M2
=
0
Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to one decimal place and your P-value to three decimal places.)
t =
P-value =
Transcribed Image Text:A research article describes a study that investigated the relationship between depression and chocolate consumption. Participants in the study were 931 adults who were not currently taking medication for depression. These participants were screened for depression using a widely used screening test. The participants were then divided into two samples based on the score on the screening test. One sample consisted of people who screened positive for depression, and the other sample consisted of people who did not screen positive for depression. Each of the study participants also completed a food frequency survey. The researchers believed that the two samples were representative of the two populations of interest-adults who would screen positive for depression and adults who would not screen positive. The paper reported that the mean number of servings of chocolate for the sample of people that screened positive for depression was 8.44 servings per month, and the sample standard deviation was 14.82. For the sample of people who did not screen positive for depression, the mean number of servings per month was 5.29, and the standard deviation was 8.78. The paper did not say how many individuals were in each sample, but for the purposes of this exercise, you can assume that the 931 study participants were divided into 311 who screened positive for depression and 620 who did not screen positive. Carry out a hypothesis test to confirm the researchers' conclusion that the mean number of servings of chocolate per month for people who would screen positive for depression is greater than the mean number of chocolate servings per month for people who would not screen positive for depression. (Use α = 0.05. Use μ₁ for people who would screen positive for depression and μ for people who would not screen positive.) State the appropriate null and alternative hypotheses. Ho: M₁ - M₂ < 0 Ha M₁ - M₂ > 0 O Ho H1 H2 = 0 - Ha H1 H20 O Ho H1-H2=0 Ha: μ₁ - μ2 % 0 ○ Ho: H1 - μ₂ > 0 Ha M₁ - M₂ = 0 O Ho: H₁₂ 0 Ha M1-M2 = 0 Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value =
Expert Solution
steps

Step by step

Solved in 4 steps with 11 images

Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax