A researcher hypothesizes that the administration of Trintellix, a new treatment for clinical depression, will decrease the number of depressive episodes experienced per week. PIDPre-treatmentPost-treatment142232332421544641 What is the appropriate statistical test to use for this study? In decimal form, express the calculated statistic. Round to the nearest hundredths. If alpha criteria is set at 0.05, is there a treatment effect? The image is a standard t-distribution table which is commonly used in statistical analysis to determine the critical t-values for hypothesis testing. Below is a transcription and detailed explanation of the table contents:### t Table- **cum. prob (Cumulative Probability)** - **one-tail** (Alpha level for one-tailed tests) - **two-tails** (Alpha level for two-tailed tests)- **Headers for t-values:** - \( t_{.50}, t_{.25}, t_{.20}, t_{.15}, t_{.10}, t_{.05}, t_{.025}, t_{.01}, t_{.005}, t_{.001}, t_{.0005} \)- **Degrees of Freedom (df):** This is the leftmost column of the table.- **t-values for each df:** Each value corresponds to a specific cumulative probability under the t-distribution curve, which varies based on the degrees of freedom.### Explanation of Components:- **Degrees of Freedom (df):** Represents the number of independent values or quantities which can be assigned to a statistical distribution. In this table, df ranges from 2 to 1000.- **Confidence Levels at Bottom of Table:** Indicates the percentage of confidence (50% to 99.9%) corresponding to the two-tailed t-values. This helps in determining the confidence interval for the dataset being analyzed.- **Highlighted Rows:** Certain rows in the table are shaded blue to signify common degrees of freedom, making it easier for users to locate frequently used values.This table aids in statistical analysis by providing critical t-values necessary for conducting hypothesis tests and forming confidence intervals, particularly when the sample size is small or when the population standard deviation is unknown.

Answered: A researcher hypothesizes that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Question

A researcher hypothesizes that the administration of Trintellix, a new treatment for clinical depression, will decrease the number of depressive episodes experienced per week.

PID	Pre-treatment	Post-treatment
1	4	2
2	3	2
3	3	2
4	2	1
5	4	4
6	4	1

What is the appropriate statistical test to use for this study?

In decimal form, express the calculated statistic. Round to the nearest hundredths.

If alpha criteria is set at 0.05, is there a treatment effect?

The image is a standard t-distribution table which is commonly used in statistical analysis to determine the critical t-values for hypothesis testing. Below is a transcription and detailed explanation of the table contents:

### t Table

- **cum. prob (Cumulative Probability)**
- **one-tail** (Alpha level for one-tailed tests)
- **two-tails** (Alpha level for two-tailed tests)

- **Headers for t-values:**
- \( t_{.50}, t_{.25}, t_{.20}, t_{.15}, t_{.10}, t_{.05}, t_{.025}, t_{.01}, t_{.005}, t_{.001}, t_{.0005} \)

- **Degrees of Freedom (df):** This is the leftmost column of the table.

- **t-values for each df:** Each value corresponds to a specific cumulative probability under the t-distribution curve, which varies based on the degrees of freedom.

### Explanation of Components:

- **Degrees of Freedom (df):** Represents the number of independent values or quantities which can be assigned to a statistical distribution. In this table, df ranges from 2 to 1000.

- **Confidence Levels at Bottom of Table:** Indicates the percentage of confidence (50% to 99.9%) corresponding to the two-tailed t-values. This helps in determining the confidence interval for the dataset being analyzed.

- **Highlighted Rows:** Certain rows in the table are shaded blue to signify common degrees of freedom, making it easier for users to locate frequently used values.

This table aids in statistical analysis by providing critical t-values necessary for conducting hypothesis tests and forming confidence intervals, particularly when the sample size is small or when the population standard deviation is unknown.

Expert Solution

Step 1

A researcher hypothesizes that the administration of Trintellix, a new treatment for clinical depression, will decrease the number of depressive episodes experienced per week.

Here, the two samples are related.

That is, the number of depressive episodes are tested before the treatment and after the treatment.

Hence, the suitable test is paired t test.