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 their test score. 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 per month of chocolate for the sample of people that screened positive for depression was 8.37, and the sample standard deviation was 14.85. For the sample of people who did not screen positive for depression, the mean was 5.27, and the standard deviation was 8.77. 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 included 311 who screened positive for depression and 620 who did not screen positive. **Find the test statistic

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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 their test score. 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 per month of chocolate for the sample of people that screened positive for depression was 8.37, and the sample standard deviation was 14.85. For the sample of people who did not screen positive for depression, the mean was 5.27, and the standard deviation was 8.77. 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 included 311 who screened positive for depression and 620 who did not screen positive.

**Find the test statistic 

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 their test score. 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 per month of chocolate for the sample of people that screened positive for depression was 8.37, and the sample standard
deviation was 14.85. For the sample of people who did not screen positive for depression, the mean was 5.27, and the standard deviation was 8.77. 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 included 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. (Use a = 0.05. Use µ, for people who would screen positive for depression and u, for people who would not
screen positive.)
State the
ppropriate null and alternative hypo
eses.
n USE SALT
O Ho: H1- H2# 0
Hai H1 - 42 =
Ho: H1 - H2 < 0
Ho: H1 - 42 = 0
Hai H1- H2 # 0
Ho: H1 - 42 = 0
Ha: 41 - H2 > 0
O Ho: H1- H2 > o
Hai H1- Hz = 0
Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.)
t =
4.417
P-value =
0.000
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 their test score. 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 per month of chocolate for the sample of people that screened positive for depression was 8.37, and the sample standard deviation was 14.85. For the sample of people who did not screen positive for depression, the mean was 5.27, and the standard deviation was 8.77. 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 included 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. (Use a = 0.05. Use µ, for people who would screen positive for depression and u, for people who would not screen positive.) State the ppropriate null and alternative hypo eses. n USE SALT O Ho: H1- H2# 0 Hai H1 - 42 = Ho: H1 - H2 < 0 Ho: H1 - 42 = 0 Hai H1- H2 # 0 Ho: H1 - 42 = 0 Ha: 41 - H2 > 0 O Ho: H1- H2 > o Hai H1- Hz = 0 Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = 4.417 P-value = 0.000
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