Question

A academic tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring. Tutoring After 3.2 2.0 3.6 3.3 3.6 2.5 2.6 3.0 2.8 (a) Test whether or not her tutoring is effective at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.) C- State the decision to retain or reject the null hypathesis. O Retain the null hypothesis. Reject the null hypothesis. b) Compute effect size using estimated Cohen's d. (Round your answer to two decimal places) You may need to use the appropriate table in Appendix C to answer this question. Additional Materials aBoak

Answer 1

$Let~d_i=difference~between~the~grades~for~i^{th}~student~prior~to~and~after~receiving\\ her~tutoring.\\ \mu_d=True~mean~difference.\\ Null~hypothesis,~H_0:~\mu_d=0~vs.~Alternative~hypothesis,~H_1:~\mu_d<0\\ Here,~d_i=x_i-y_i:~-0.7,~ -0.3,~ -0.5,~ -0.3,~ -0.8\\ where,~x_i=grade~of~ith~student~before~tuition\\ y_i=grade~of~ith~student~after~tuition\\ \bar{d}=\frac{1}{5}\sum_{i=1}^5d_i=-0.520,~s_d=\sqrt{\frac{1}{4}\sum_{i=1}^5(d_i-\bar{d})^2}=0.228\\ (a)~t=\frac{\sqrt{5}(\bar{d})}{s_d}=-5.100\\ p-value=P(t<-5.100|t\sim t_4)= 0.003<0.05\\ So,\\ Reject~the~null~hypothesis.\\ (b)~d=|\bar{d}|/s_d=0.520/0.228=2.28$

Paired T-Test: Before, After

Paired T for Before - After

N Mean StDev SE Mean
Before 5 2.800 0.255 0.114
After 5 3.320 0.295 0.132
Difference 5 -0.520 0.228 0.102