16) An instructor is interested in comparing students\' Spanish oral skills to t

Question

16) An instructor is interested in comparing students' Spanish oral skills to their writing skills for students in a high school who are taking Spanish. An experiment is conducted with 14 students who are taking Spanish in that high school. Students are giving both a written and an oral exam in Spanish. To avoid order effects, 7 randomly selected students are first tested with a written exam and a day later with an oral exam. The other 7 students are tested in reverse order. The table below summarize descriptive statistics for the grades of the two tests and the difference of two grades Write Talk Write - Talk14 Mean 4.17 2.82 1.35 Std. Deviation 2.05 1.83 1.22 Suppose all required conditions are satisfied. Construct a 95% confidence interval to estimate the mean of difference grades between the two testing methods for all students who are taking Spanish in that high school. Select the closest answer A) (-0.09, 2.79) B (-0.16, 2.86) C) (0.65, 2.05) D) (0.71,1.99) E) (0.32, 2.38)

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =1.22/(14)1/2 =0.3261

for 95% CI and (n-1=13) degree of freedom critical value of t =2.1604

therefore 95% confidence interval =sample mean -/+ t*std error =1.35 -/+ 2.1604*0.3261=0.65 ; 2.05

(Note: You can use tcdf function for calculatiing crtiical value of t from ti -84 calculator)

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