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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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How would I solve this? It involves interpretation of p-values, kurtosis, and significance levels?
Transcribed Image Text: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
91.7
56.8
82.5
76.9
70.3
90.1
74.1
88.4
87.5
88.3
90.4
93.7
82.5
To begin, some basic descriptive statistics for each group and assumption test results are given below:
> stat.desc (hybrid)
nbr.val
nbr.null
nbr.na
nin
range
34.700
пах
sum
7.000
0.000
0.000
56.800
91.500
573.400
median
SE.mean CI. mean.0.95
mean
var
std.dev
coef.var
88.300
81.914
4.624
11.314
149.645
12.233
0.149
skeu. 25E
normtest.p
skeuness
kurtosis
kurt. 2SE
norntest.W
-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
пах
sum
9.000
0.000
0.000
70.300
93.700
764.900
nedian
mean
SE.mean CI.mean.0.95
var
std.dev
coef.var
87.500
84.989
2.777
6.404
69.404
8.331
0.098
skeuness
skeu. 2SE
kurtosis
kurt. 2SE
normtest.W
normtest.p
-0.572
-0.399
-1.337
-0.478
0.889
0.195
> shapiro.test (hybrid)
Shapiro-Wilk nornality test
w - 0.78861, p-value - 0.03155
> shapiro.test (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.
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