Version of the test (A or B), the score of the test, and the time to complete th
ID: 3258969 • Letter: V
Question
Version of the test (A or B), the score of the test, and the time to complete the test were measured.
test 1 form
a
40
23
b
84
46
use this date to complete the questions below. sample data for a group of 70 MAT 110 students. Each test was given in two forms, Form A and Form B. Completion times and scores earned are recorded for each of the 70 students. (Student names are fake to protect privacy, but the times and scores are real
Show all work including the original claim, hypotheses, critical value(s), test statistic, the name of the sampling distribution, and a description or picture the rejection region(s). You must also state your decision and interpret it in the context of the problem.
1. One student was upset with her grade on Test 2 and thought the test was too difficult. In her anger, she said, “There is no way the class average on this test was higher than a C.” Can you conclude at a 0.05 level of significance that the average score on Test 2 was no higher than a 79? (7 pts)
2. Another student was also upset. He thought that Test 2 was too long and said, “More than half of the class was still testing when there were only 10 minutes left!” (Students are allowed 90 minutes to complete the test.) Can you conclude at a 0.01 level of significance that a majority of the students were still testing at the 80-minute mark?
3. If your decision for the hypothesis test you performed for Problem 2 was incorrect, what type of error would it be (Type I or Type II)? Explain what this error means in the context of this situation.
4. One of the MAT 110 instructors thought that Test 2 was easier than Test 1. She said, “I think students scored a lot higher on the second test.” Can you conclude at a 0.05 level of significance that the scores for Test 2 were higher than for Test 1?
The following data was collected from a MAT 110 class.Version of the test (A or B), the score of the test, and the time to complete the test were measured.
Name Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7 Student 8 Student 9 Student 10 Student 11 Student 12 Student 13 Student 14 Student 15 Student 16 Student 17 Student 18 Student 19 Student 20 Student 21 Student 22 Student 23 Student 24 Student 25 Student 26 Student 27 Student 28 Student 29 Student 30test 1 form
a a a a b b b b a b b a b a b b a b b a a b a b b a b a aa
Test 1 Score 93 79 79 94 38 93 100 88 66 89 62 99 65 93 69 90 64 95 88 70 80 97 98 99 95 57 68 86 7640
Test 1 Time 45 31 44 34 71 31 39 33 33 48 66 33 74 64 38 18 42 31 48 36 33 61 33 34 37 67 45 38 3823
Test 2 Form b a a a a a a b b b b b a a b b b b a a a a a b b a b b ab
Test 2 Score 89 91 87 87 57 96 99 84 76 93 67 96 73 86 48 91 93 98 84 70 64 94 97 99 96 83 98 99 9084
Test 2 Time 53 27 25 26 82 27 32 33 29 50 65 24 90 48 29 26 38 29 41 35 33 83 25 36 36 45 26 34 7646
use this date to complete the questions below. sample data for a group of 70 MAT 110 students. Each test was given in two forms, Form A and Form B. Completion times and scores earned are recorded for each of the 70 students. (Student names are fake to protect privacy, but the times and scores are real
Show all work including the original claim, hypotheses, critical value(s), test statistic, the name of the sampling distribution, and a description or picture the rejection region(s). You must also state your decision and interpret it in the context of the problem.
1. One student was upset with her grade on Test 2 and thought the test was too difficult. In her anger, she said, “There is no way the class average on this test was higher than a C.” Can you conclude at a 0.05 level of significance that the average score on Test 2 was no higher than a 79? (7 pts)
2. Another student was also upset. He thought that Test 2 was too long and said, “More than half of the class was still testing when there were only 10 minutes left!” (Students are allowed 90 minutes to complete the test.) Can you conclude at a 0.01 level of significance that a majority of the students were still testing at the 80-minute mark?
3. If your decision for the hypothesis test you performed for Problem 2 was incorrect, what type of error would it be (Type I or Type II)? Explain what this error means in the context of this situation.
4. One of the MAT 110 instructors thought that Test 2 was easier than Test 1. She said, “I think students scored a lot higher on the second test.” Can you conclude at a 0.05 level of significance that the scores for Test 2 were higher than for Test 1?
Explanation / Answer
1.
Original Claim - Class average on test 2 was not higher than a grade C.
Null Hypothesis H0: The average score on Test 2 was higher than a 79.
Alternative Hypothesis H1: The average score on Test 2 was no higher than a 79.
The degree of freedom = 30 - 1 = 29
t statistic at significance level of 0.05 and degree of freedom, 29 is -1.7 (As this is lower tail test)
Critical values of t is -1.7
The sampling distribution is a normal distribution.
Rejection region is t < - 1.7
Average score of test t2 is 85.63
Standard deviation of score 2 is 13.3
Standard error = 13.3/sqrt(30) = 2.43
t = (85.63-79)/2.43 = 2.73
As, the observed value of t does not lie in the rejection region, we accept the null hypothesis and conclude that the average score on Test 2 was higher than a 79.
2.
Original Claim - Majority of the students in test 2 were still testing at the 80-minute mark.
Null Hypothesis H0: At 80-minute mark, less than 50% of the students were testing in test 2.
Alternative Hypothesis H1: At 80-minute mark, more than 50% of the students were testing in test 2.
Number of students who were testing at 80-minute mark is 3.
Proportion of students who were testing at 80-minute mark = 3/30 = 0.1
Standard error = sqrt(0.1*(1-0.1)/30) = 0.055
t statistic at significance level of 0.01 and degree of freedom, 29 is 2.46 (As this is upper tail test)
Critical values of t is 2.46
The sampling distribution is a normal distribution.
Rejection region is t > 2.46
t = (0.1-0.5)/0.055 = -7.27
As, the observed value of t does not lie in the rejection region, we accept the null hypothesis and conclude that at 80-minute mark, less than 50% of the students were testing in test 2.
3.
In problem 2, we are accepting the null hypothesis. So, if our decision for the hypothesis test we performed for Problem 2 was incorrect, then we accepted a false null hypothesis which is a type II error. This means that at 80-minute mark, more than 50% of the students were testing in test 2 but we concluded that at 80-minute mark, less than 50% of the students were testing in test 2.
4.
Original Claim - Students scored a higher score on the second test as compared with test 1
Null Hypothesis H0: Score in test 1 and test 2 are equal.
Alternative Hypothesis H1: Score of test 2 is greater than score of test 1.
Average score of test 1 = 80.33
Average score of test 2 = 85.63
Standard deviation of score of test 1 = 17.13
Standard deviation of score of test 2 = 13.3
Standard error, SE = sqrt[ (s12/n1) + (s22/n2) ]
= sqrt[ (17.132/30) + (13.32/30) ] = 3.96
Degree of freedom DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (17.132/30 + 13.32/30)2 / { [ (17.132 / 30)2 / (30 - 1) ] + [ (13.32 / 302)/ (30- 1) ] } = 55 (Rounded to nearest integer)
t statistic at significance level of 0.05 and degree of freedom, 55 is 1.67 (As this is upper tail test)
Critical values of t is 1.67
The sampling distribution is a normal distribution.
Rejection region is t > 1.67
t = (85.63-80.33)/3.96 = 1.34
As, the observed value of t does not lie in the rejection region, we accept the null hypothesis and conclude that at 5% significance level, score in test 2 is statistically same as score in test 1.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.