Question

A researcher is interested in whether sports participation results in higher self-esteem in girls. She collects self-esteem scores from 20 midd le school girls who either do or do not participate in sports and compared them. The data are below -_05): Girls with sports Girls without sports 14 136 121 81 144 169 225 169 121 289 81 64 100 81 121 81 121 64 144 121 169 10 12 13 15 13 12 17 13 Ex 1596 ΣΧ-124 N-10 F 12.4 10 X 10.2 2.55 1.69 One or two tailed? Two tailed Critical value: +/-/ ±1.96 Null Hypothesis: Alt. Hypothesis: μ.μ. ___ In words: μ1Hs In words:

Answer 1

$Pooled~sample~variance=s_0^2=\frac{9*2.55^2+9*1.69^2}{18}=4.6793\\ s_0=2.1632\\ Here~we~assume,~the~data~come~from~two~independent~normal~populations~\\ with~unknown~but~equal~variances.\\ Then~t_{obs}=\frac{12.4-10.2}{2.1632\sqrt{\frac{2}{10}}}=2.2741\\ Critical~value=t_{0.05,18}=1.7341\\ Since~t_{obs}>t_{0.05,18},~hence~we~reject~H_0~at~5\%~level~and~conclude~that~there~is\\ enough~evidence~that~sports~participation~results~in~higher~self~esteem~in~girls.$$Let~\mu_1=True~mean~self~esteem~scores~of~Girls~with~sports\\ \mu_2=True~mean~self~esteem~scores~of~Girls~without~sports\\ Null~hypothesis:~H_0:\mu_1=\mu_2\\ i.e.~there~is~no~difference~between~true~average~scores~of~self\\ esteem~of~girls~with~and~without~sports.\\ Alternative~hypothesis,~H_a:\mu_1>\mu_2\\ true~average~score~of~self\\ esteem~of~girls~with~f~self\\ esteem~of~girls~with~and~with~sports~is~greater~than~the~true~average\\ score~of~girls~without~sports.~\\ Hence~it~is~a~right~tail~test.$