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 fordepression 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 isgreater 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 greaterthan 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 isgreater 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 currentlytaking 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 thescore 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 screenpositive. 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 samplestandard 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 was8.78. 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 whoscreened 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 greaterthan 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 fordepression and μ for people who would not screen positive.)State the appropriate null and alternative hypotheses.Ho: M₁ - M₂ 0O Ho H1 H2 = 0-Ha H1 H20O Ho H1-H2=0Ha: μ₁ - μ2 % 0○ Ho: H1 - μ₂ 0Ha M₁ - M₂ = 0O Ho: H₁₂ 0Ha M1-M2=0Find 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 =

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 fordepression 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 isgreater 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 greaterthan 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 isgreater 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 currentlytaking 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 thescore 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 screenpositive. 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 samplestandard 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 was8.78. 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 whoscreened 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 greaterthan 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 fordepression and μ for people who would not screen positive.)State the appropriate null and alternative hypotheses.Ho: M₁ - M₂ < 0Ha M₁ - M₂ > 0O Ho H1 H2 = 0-Ha H1 H20O Ho H1-H2=0Ha: μ₁ - μ2 % 0○ Ho: H1 - μ₂ > 0Ha M₁ - M₂ = 0O Ho: H₁₂ 0Ha M1-M2=0Find 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 =

Accepted Answer

There are two independent samples screen positive and not screen positive.We have to test whether…