Answer to Question #327843 in Statistics and Probability for Jade

Question #327843

A course in mathematics is taught to 15 students by explicit method. Another group of 17 students was given the same course by means of another method. At the end of the semester, the same test was administered to each group. The 15 students under method A made an average of 85 with a standard deviation of 4, while the 17 students under method B made an average of 81 with a standard deviation of 5. Test



the null hypothesis of no significant difference in the performance of the two groups of



students at 5% level of significance.



Solution:



1. H0:



H1:



2. Level of Significance:



3.Test:



4. Critical Region:



5. Solution:



Make a decision and draw a



conclusion based from the results.



1. Decision:



2. Conclusion:

1
Expert's answer
2022-04-13T18:27:27-0400

1:H0:μ1=μ2H1:μ1μ22:α=0.053.Test:ttestn1=15n2=17xˉ1=85xˉ2=81s1=4s2=5ν=(s12n1+s22n2)21n11(s12n1)2+1n21(s22n2)2=(4215+5217)2114(4215)2+116(5217)2=29.744230T=xˉ1xˉ2s12n1+s22n2=15174215+5217=1.255594.CriticalRegion:T>tinv(1+γ2,ν)=tinv(0.975,30)=2.04225.Solution:T<2.0422Make  a  decision  and  draw  a  conclusion  based  from  the  results.1.Decision:Not  reject  H02.Conclusion:The  results  in  two  methods  are  not  significally  different1:\\H_0:\mu _1=\mu _2\\H_1:\mu _1\ne \mu _2\\2:\\\alpha =0.05\\3.Test:\\t-test\\n_1=15\\n_2=17\\\bar{x}_1=85\\\bar{x}_2=81\\s_1=4\\s_2=5\\\nu =\frac{\left( \frac{{s_1}^2}{n_1}+\frac{{s_2}^2}{n_2} \right) ^2}{\frac{1}{n_1-1}\left( \frac{{s_1}^2}{n_1} \right) ^2+\frac{1}{n_2-1}\left( \frac{{s_2}^2}{n_2} \right) ^2}=\frac{\left( \frac{4^2}{15}+\frac{5^2}{17} \right) ^2}{\frac{1}{14}\left( \frac{4^2}{15} \right) ^2+\frac{1}{16}\left( \frac{5^2}{17} \right) ^2}=29.7442\approx 30\\T=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{{s_1}^2}{n_1}+\frac{{s_2}^2}{n_2}}}=\frac{15-17}{\sqrt{\frac{4^2}{15}+\frac{5^2}{17}}}=-1.25559\\4.CriticalRegion:\\\left| T \right|>t_{inv}\left( \frac{1+\gamma}{2},\nu \right) =t_{inv}\left( 0.975,30 \right) =2.0422\\5.Solution:\\\left| T \right|<2.0422\\Make\,\,a\,\,decision\,\,and\,\,draw\,\,a\,\,conclusion\,\,based\,\,from\,\,the\,\,results.\\1.Decision:\\Not\,\,reject\,\,H_0\\2.Conclusion:\\The\,\,results\,\,in\,\,two\,\,methods\,\,are\,\,not\,\,significally\,\,different


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