3. During the pandemic, high school students had the choice of hybrid learning or being completely virtual. A study was conducted to investigate academic performance based on modality of learning (hybrid vs. fully virtual). A group of 7 hybrid students and 9 fully virtual students were examined, with GPA data (scored out of 100) being collected on each student. The data are presented below: Hybrid | Fully Virtual 91.5 92.2 81.4 56.8 76.9 90.1 88.4 88.3 91.7 82.5 70.3 74.1 87.5 90.4 93.7 82.5 To begin, some basic descriptive statisties for each group and assumption test results are given below: > stat.desc (hybrid) nbr. val nbr.null 144444 nbr.na nin range 34.700 nax Bum 7.000 0.000 0.000 56.800 91.500 573.400 atd.dev 12.233 nedian mean SE. mean CI. mean.0.95 var coef.var 88.300 81.914 4.624 11.314 149.645 0.149 akeuness akeu. 2SE kurtosia kurt.2SE noratest.W norntest.p -1.093 -0.688 -0.354 -0.111 0.789 0.032 > stat.desc (virtual, norn-T) nbr. val nbr.null nbr.na nin range 23.400 atd.dev max sum 9.000 0.000 0.000 70.300 93.700 764.900 nedian 87.500 SE. nean CI. mean.0.95 2.777 mean var coef.var 84.989 6.404 69.404 8.331 0.098 akeuness akeu. 2SE kurtosia kurt. 28E norntest.W norntest.p 0. 195 -0.572 -0.399 -1.337 -0.478 0.889 > shapiro.test (hybrid) Shapiro-Wilk nornality test W - 0.78861, p-value - 0.03155 > shapiro.teat (virtual) Shapiro-Wilk nornality test w - 0.88914, p-value - 0.1955 (a) Explain and justify (citing information from above) why a nonparametric test is appropriate here. (b) What is the name of the appropriate nonparametric test in this situation? (c) Write out the hypotheses for this nonparametric test in the context of this problem. (d) Calculate the test statistic for the nonparametric test. (e) Write the R code to calculate this test in R using a normal approximation for the p-value. (f) Suppose the p-value equals 0.5251. What conclusion do you reach regarding the hypotheses at the a = 0.05 significance level? Explain your results.
3. During the pandemic, high school students had the choice of hybrid learning or being completely virtual. A study was conducted to investigate academic performance based on modality of learning (hybrid vs. fully virtual). A group of 7 hybrid students and 9 fully virtual students were examined, with GPA data (scored out of 100) being collected on each student. The data are presented below: Hybrid | Fully Virtual 91.5 92.2 81.4 56.8 76.9 90.1 88.4 88.3 91.7 82.5 70.3 74.1 87.5 90.4 93.7 82.5 To begin, some basic descriptive statisties for each group and assumption test results are given below: > stat.desc (hybrid) nbr. val nbr.null 144444 nbr.na nin range 34.700 nax Bum 7.000 0.000 0.000 56.800 91.500 573.400 atd.dev 12.233 nedian mean SE. mean CI. mean.0.95 var coef.var 88.300 81.914 4.624 11.314 149.645 0.149 akeuness akeu. 2SE kurtosia kurt.2SE noratest.W norntest.p -1.093 -0.688 -0.354 -0.111 0.789 0.032 > stat.desc (virtual, norn-T) nbr. val nbr.null nbr.na nin range 23.400 atd.dev max sum 9.000 0.000 0.000 70.300 93.700 764.900 nedian 87.500 SE. nean CI. mean.0.95 2.777 mean var coef.var 84.989 6.404 69.404 8.331 0.098 akeuness akeu. 2SE kurtosia kurt. 28E norntest.W norntest.p 0. 195 -0.572 -0.399 -1.337 -0.478 0.889 > shapiro.test (hybrid) Shapiro-Wilk nornality test W - 0.78861, p-value - 0.03155 > shapiro.teat (virtual) Shapiro-Wilk nornality test w - 0.88914, p-value - 0.1955 (a) Explain and justify (citing information from above) why a nonparametric test is appropriate here. (b) What is the name of the appropriate nonparametric test in this situation? (c) Write out the hypotheses for this nonparametric test in the context of this problem. (d) Calculate the test statistic for the nonparametric test. (e) Write the R code to calculate this test in R using a normal approximation for the p-value. (f) Suppose the p-value equals 0.5251. What conclusion do you reach regarding the hypotheses at the a = 0.05 significance level? Explain your results.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 27PPS
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