A school psychologist is interested in determining if children with attention deficit hyperactivity disorder (ADHD) learn better if English literature is read to them rather than having them read the material alone by themselves. A random sample of 10 sixth graders with ADHD is selected and divided into two groups of n=9. One of the groups has a story read to them (Listening Group) and the other reads the story alone by themselves (Reading Group). A test on the story is given after each group has finished reading or hearing the story. The following scores were obtained with 20 being a perfect score.what is the pooled variance? ## t-Test: Two-Sample Assuming Equal VariancesThis table presents the results of a two-sample t-test assuming equal variances. The groups are labeled as G1 and G2.### Descriptive Statistics- **Mean** - G1: 8.77777778 - G2: 11.44444444- **Variance** - G1: 3.944444444 - G2: 3.277777778- **Observations** - G1: 9 - G2: 9### Pooled Variance- **Pooled Variance:** 3.611111111### Hypothesized Mean Difference- **Hypothesized Mean Difference:** 0### Degrees of Freedom- **df:** 16### Test Statistics- **t Stat:** -2.97683363### Probability and Critical Values- **P(T<=t) one-tail:** 0.004449553- **t Critical one-tail:** 1.745883676- **P(T<=t) two-tail:** 0.008899105- **t Critical two-tail:** 2.119905299### Interpretation of Results- **Mean:** The average value for G1 is approximately 8.78 and for G2 it is approximately 11.44.- **Variance:** The variability of data points is slightly higher in G1 (3.94) compared to G2 (3.28).- **Observations:** Both G1 and G2 have 9 data points.- **Pooled Variance:** This is an average measure of variability between the two groups, which is approximately 3.61.- **t Stat:** The calculated test statistic is -2.97683363.- **P-Value (P(T<=t)):** For a one-tail test, the p-value is 0.004449553, which is very small, suggesting that we might reject the null hypothesis if we are performing a one-tailed test.- **Critical t-Values:** The critical t-values for one-tail and two-tail tests at a certain significance level are 1.745883676 and 2.119905299, respectively.These results indicate that there is a statistically significant difference between the means of the two groups at the chosen significance level. **Two-sample t-test, Independent Groups****Dataset:**The dataset is divided into two groups: **Reading Group** and **Listening Group**.| Reading Group | Listening Group ||---------------|-----------------|| 10 | 15 || 10 | 12 || 7 | 13 || 12 | 11 || 8 | 10 || 8 | 9 || 10 | 11 || 9 | 10 || 11 | 11 |**Calculations and Statistical Measures:**- **Count (n):** Represents the number of data points in each group.- **Mean:** The average value of the data points in each group.- **DEVSQ (SS):** The sum of squared deviations from the mean.- **STDEV.S:** The standard deviation of the sample data.- **df:** Degrees of freedom for the test.- **S(M1-M2):** Standard error of the difference between the two means.- **alpha:** The significance level (commonly set at 0.05).- **t_crit:** The critical value of t at the given alpha.- **t_obs:** The observed t-value calculated from the data.- **Cohen's d:** Measures the effect size.- **r^2:** Coefficient of determination.**Decision:**Based on hypotheses testing,- The null hypothesis (Ho) is tested.- Depending on the observed t-value (t_obs) and critical t-value (t_crit), we either: - **Reject Ho:** If the t_obs falls in the critical region determined by t_crit. - **Fail to Reject Ho:** If the t_obs does not fall in the critical region.**Conclusion:**- If "Reject Ho" is indicated, it suggests there is a significant difference between the Reading and Listening groups.- If "Fail to Reject Ho" is indicated, it suggests there is no significant difference between the Reading and Listening groups.**Graph/Diagram Explanation:**No specific graph or diagram is depicted in the current image. The image contains a table of columns with numerical data points for two groups, and subsequent fields for statistical measures intended to perform a t-test analysis.This information would typically be presented alongside instructional content explaining how to conduct a two-sample t-test

Reading Group Listing Group 13.44468889 10 15 0.44448889 10 12 2.77788889 7 13…

Answered: school psychologist is interested in…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P