1. A professor believes that 40% of Stat students will get 90% or above, 30% wil
ID: 3229212 • Letter: 1
Question
1. A professor believes that 40% of Stat students will get 90% or above, 30% will get between 80% and 89.9%, 30% will get 79.9% or below. Is she right at 0.01 level of significance?
2. Is the percentage of classes students miss related to the Overall Grade%?
3. Predict a student's grade who missed 40% of classes? Can you predict a student's grade who missed 65% of classes? 4. Are the three exams' averages different at 0.05 level of significance? At 0.1 level of significance?
Student ID Exam1 Exam2 Exam3 Overall % % Absences 1 99% 97% 99% 98% 18.2% 2 90% 67% 73% 77% 18.2% 3 100% 93% 103% 99% 9.1% 4 87% 81% 60% 76% 18.2% 5 77% 71% 83% 77% 36.4% 6 97% 103% 101% 100% 0.0% 7 90% 81% 80% 84% 27.3% 8 77% 88% 80% 82% 27.3% 9 93% 53% 70% 72% 54.5% 10 100% 102% 103% 102% 9.1% 11 93% 87% 63% 81% 9.1% 12 97% 94% 87% 92% 0.0% 13 93% 90% 83% 89% 9.1% 14 105% 96% 97% 99% 9.1% 15 93% 81% 90% 88% 0.0% 16 97% 96% 100% 98% 0.0% 17 83% 90% 93% 89% 0.0% 18 83% 101% 90% 91% 9.1% 19 93% 103% 103% 100% 0.0% 20 97% 96% 93% 95% 0.0% 21 97% 93% 97% 95% 0.0% 22 83% 94% 77% 85% 27.3% 23 73% 67% 83% 74% 18.2% 24 100% 85% 69% 85% 18.2% 25 63% 78% 67% 69% 45.5% 26 63% 43% 73% 60% 54.5% 27 90% 85% 57% 77% 36.4% 28 60% 85% 87% 77% 45.5% 29 97% 71% 100% 89% 54.5% 30 63% 57% 55% 58% 45.5% 31 80% 85% 83% 83% 36.4% 32 90% 94% 103% 96% 27.3% 33 77% 88% 83% 83% 0.0% 34 103% 93% 100% 99% 0.0% 35 97% 102% 100% 99% 0.0% 36 93% 87% 93% 91% 0.0% 37 93% 87% 93% 91% 9.1% 38 77% 85% 45% 69% 45.5% 39 73% 90% 83% 82% 9.1% 40 100% 96% 83% 93% 27.3% 41 90% 85% 100% 92% 0.0% 42 80% 68% 75% 74% 27.3% 43 100% 102% 78% 93% 18.2% 44 73% 75% 83% 77% 27.3% 45 70% 63% 60% 64% 27.3% 46 60% 71% 57% 63% 54.5% 47 77% 71% 63% 70% 27.3% 48 80% 68% 70% 73% 36.4% 49 97% 102% 100% 99% 9.1% 50 73% 78% 80% 77% 0.0% 51 93% 87% 70% 83% 27.3% 52 77% 67% 60% 68% 27.3% 53 77% 67% 55% 66% 27.3% 54 100% 93% 97% 96% 18.2% 55 97% 102% 103% 101% 9.1% 56 83% 87% 60% 77% 54.5% 57 97% 87% 100% 95% 9.1% 58 100% 93% 97% 96% 0.0% 59 80% 85% 60% 75% 27.3% 60 93% 94% 97% 95% 27.3% 61 77% 90% 90% 86% 9.1% 62 87% 90% 93% 90% 18.2% 63 83% 78% 85% 82% 0.0% 64 103% 87% 93% 94% 9.1% 65 87% 63% 97% 82% 45.5% 66 77% 85% 73% 78% 45.5% 67 97% 90% 87% 91% 27.3% 68 87% 85% 90% 87% 0.0% 69 93% 90% 105% 96% 9.1% 70 80% 78% 77% 78% 9.1% 71 100% 90% 83% 91% 45.5% 72 100% 90% 80% 90% 27.3% 73 100% 90% 87% 92% 36.4% 74 93% 85% 80% 86% 54.5% 75 97% 67% 63% 76% 36.4% 76 100% 90% 103% 98% 9.1% 77 93% 99% 75% 89% 9.1% 78 80% 85% 77% 80% 36.4% 79 100% 102% 97% 99% 9.1% 80 100% 90% 97% 96% 0.0% 81 93% 99% 77% 90% 9.1% 82 93% 94% 97% 95% 9.1% 83 90% 96% 83% 90% 9.1% 84 100% 99% 100% 100% 18.2% 85 97% 99% 90% 95% 18.2% 86 80% 63% 80% 74% 18.2% 87 87% 68% 80% 78% 9.1% 88 77% 90% 83% 83% 9.1% 89 70% 75% 97% 80% 18.2% 90 93% 85% 77% 85% 9.1% 91 97% 90% 83% 90% 9.1% 92 90% 96% 100% 95% 9.1%Explanation / Answer
#1 A professor believes that 40% of Stat students will get 90% or above, 30% will get between 80% and 89.9%, 30% will get 79.9% or below. Is she right at 0.01 level of significance?
H0:p1=0.4, p2=0.3, p3=0.3
H1: Atleast one percentage is different.
There are three categories, 90% or above, between 80% and 89.9% and 79.9% or below.
df=k-1=3-1=2
Critical value of chi square at =0.01 and df=2 is 9.210. Reject null hypothesis if ² > 9.210.
Count number of students fall in each category and write frequency in O.
²= (O-E)²/E = 1.514
Since ² is less than 9.210, fail to reject null hypothesis. There is sufficient evidence to support professor's believe.
Category p O E=np (O-E)²/E 90% 0.4 42 36.8 0.735 80%-89.9% 0.3 23 27.6 0.767 79.9% 0.3 27 27.6 0.013 Sum 1 92 92 1.514Related Questions
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