Question

please show all 6 steps with calculations!

Assignment # 1 3: Between-Subjects ANOVA Instructions: For each research scenario, please complete the source table and conduct a hypothesis test at a-05 significance level using a between-groups ANOVA to determine if one group is different from the others. Please be sure to show your work when performing mathematical operations. Please round all calculations to two decimal places. Scenario 1. Dr. Smith has developed a new way to administer a GRE prep workshop to psychology and psychological science majors at her university. She wants to know if the effectiveness of her new program is different from her old one, so she compares the average GRE performance of her students from last year to the average GRE performance of this year's students. To keep things simple, Dr. Smith adds each students' GRE quantitative and GRE verbal scores to get a single composite GRE score for each student. Although 20 students take part in her GRE prep workshop each year, she only has data on 7 students for each year. Ist year workshop GRE scores (n 7): 280, 290, 300, 300, 300, 300, 310. M-297, s- 9.5 year workshop GRE scores (n Source Between-groups Within-groups Total 7): 290, 300, 310, 310, 320, 320, 320. M-310, s 11.55 df MS Step 1. Describe the populations, distribution and assumptions. For this step, please only test the assumption on homogeneity of variances First Group s Second Group s Step 2. State the null and research hypotheses. Step 3. Determine the characteristcs of the comparison distribution. Step 4. Determine the critical values. Step 5. Calculate the test statistic. Assignment # 13: Between-Subjects ANOVA Step 6. Make a decision and report your findings in APA format. Calculate the effect size for this ANOVA using the following equation: Effect size in R2: R2 = ssserwem- SStotal

Answer 1

$Step~1:\\Population:~The~students~at~Dr.~Smith's~University\\ We~assume~the~GRE~scores~of~students~follow~normal~distribution.\\ Let~\sigma_1^2=population~variance~of~first~group\\ \sigma_2^2=population~variance~of~second~group\\ Null~hypothesis,~H_0:\sigma_1^2=\sigma_2^2\\ Alternative~hypothesis,~H_1:\sigma_1^2\neq \sigma_2^2\\ Test~statistic=F=\frac{s_1^2}{s_2^2}=9.51^2/11.55^2=0.6779\\ Critical~values:F_{0.975,6,6}=0.1718~and~F_{0.025,6,6}=5.8198\\ Since~Value~of~F\in (0.1718,~5.8198)~so~we~fail~to~reject~H_0~and\\ assumption~on~homogeneity~of~variances~is~valid.\\ Step~2:\\ Null~hypothesis:\mu_1=\mu_2\\ Alternative~hypothesis:\mu_1\neq \mu_2\\ where,~\mu_1=population~mean~of~GRE~scores~of~first~Group\\ \mu_2=population~mean~of~GRE~scores~of~second~Group\\$

Step 3:

Probability Plot of GRE Score Normal-95% CI Mean 303.6 StDev 12.16 14 0.486 P-Value 0.189 AD 260 270 280 290 300 310 320 330 340 350 GRE SCore

From the above plot we conclude that normality assumption is valid.

$Step 4:~F_{0.05,1,12}=4.7472\\ Step~5:\\ SSB=sum~of~square~between~groups\\ =7*(297^2+310^2)-14*((297+310)/2)^2=591.5\\ SSW=sum~of~square~within-groups=6*9.51^2+6*11.55^2=1343.056 \\ SST=total~sum~of~square=SSB+SSW=591.5+1343.056=1934.556\\ \begin{matrix} Source& SS & df & MS=SS/df &F \\ \hline Between-groups &591.5 &1& 591.5 & 591.5/111.9213=5.2850\\ Within-groups&1343.056 & 12 & 1343.056/12=111.9213 & \\ \hline Total &1934.556 &13 & & \end{matrix}\\ Value~of~test~statistic=F=5.2850\\ Step~6:\\ Since~value~of~F>4.7472~so~we~we~reject~H_0~at~5\%~level~of~significance~and~conclude~that\\ these~two~groups~are~significantly~different.\\ R^2=591.5/1934.556=0.3058$