Question

A college student is interested in whether there is a difference between male and female students in the amount of time they spend studying each week. The student gathers information from a random sample of male and female students on campus. The amounts of time spent studying are normally distributed. The following includes the data and the questions.

Males Females 27 25 25 9 10 16 22 14. a. What statistical test should be used to analyze these data? b. Identify H, and H for this study. C. Conduct the appropriate analysis. d. Should H, be rejected? What should the researcher conclude? e. If significant, compute and interpret the effect size. conting

Answer 1

curitaniwlentitudinis; we have two Independent samples. we need to best whether awelage time spend by males and fenates are different al not (a) Since we have two independent samples, population is normally distributed we use t test Independent samples. Also sample size, n=1 no at which is less than 30 ce Null hypothesis: The statement which contain, no significant difference between the groups . Alternative hapothesis: The Statement which contain significant difference between the groups Null hypothesis, Ho: y = fly against the alternative - hypothesis, Hi. +42 y a awerage time spend by males. May average time spend by females () from the sample information provided, Sample means for males, the * - 27+25+19 +10 H6 +2244 = 133 cmq Sample means of females, Fe=25+29+18+23+20+15+19. = 149 - 21.2857 sample standard deviation of maler, s= (2-17 (65-777 ...+117-79 - 14(224) = 373195 - 6. 1101 *

i wide webs i blok Wa WH Sa (65-21.2857)2+(29–21.28577----19-21-285132 1331 4281) 22:23T= 4.7157 - we will perform a two-tailed test foo whech a t test - for two population means, with two independent samples with unknown population standard deviations will be used Rejection region :- Based on the information poovided, the significance lead is 2=0.05, and the degrees of freedom is af- mitha-2 = 7+7-2 = 12 The critical value for this two tailed test is tc=toos n = 2.179 (from t table). The rejection region for this two-failed test is, R=St Hl>2.1797 test statistic; t= X-Tz [6-1)²+2-12²( A l Rith- 19- 21.2857 02784 | 61-106-1101246-024.7157 (1417 12 & since it is observed that It=1-07841= 40.784 <te- 2.179, it is concluded that the null hepothesis is not rejected. That is there is not enough evidence to claim

I that average time ofend. by males is different than the findes I That is differente in time spend by males are females L is not significant. (e) Since not ignificant, effect size is rendent.