Open Lab Visits data. Is it reasonable to claim that students with 8 or more vis
ID: 3053269 • Letter: O
Question
Open Lab Visits data. Is it reasonable to claim that students with 8 or more visits to open lab sessions have average final grade greater than 78? 5. What test/procedure did you perform? (5 points) a. One-sided t-test b. Two sided t-test c. Regression d. Confidence Interval 6. What is the P-value/margin of error? (5 points) a. 6.540715 b. 3.622127 c. 7.568275 d. 4.845943 7. What is the Statistical interpretation? (5 points) a. The P-value is much greater than 5% thus we cannot claim that the averages are different. b. The P-value is much greater than 5% thus we are very certain that the slope is not zero. c. The P-value is much greater than 5% thus we cannot claim that number of visits to open lab sessions is related to final grade. d. The prediction interval for the true average final grade of students with 8 or more visits to open lab is [78.64454, 85.88879] 8. What is the conclusion? (5 points) a. We are confident that more visits to open lab sessions lead to higher final grades. b. We cannot be confident that more visits to open lab sessions lead to higher final grades. c. We are confident that students with 8 or more visits to open lab sessions have average final grade greater than 78. d. None of these. DATA: # of OpenLab visits Final grade 2 40 8 85 10 80 9 84 15 90 7 72 5 50 4 59 8 85 10 70 7 66 7 70 5 63 4 60 4 59 11 79 3 82 9 90 10 82 9 76 14 85 6 73 5 41 4 56 8 80 10 70 7 66 9 88 5 65 4 70 4 62 11 90
Explanation / Answer
(a) We would perform (a) one sided t-test
This is because the counter claim is of the form > type. So, technically a right tailed test would be appropriate.
(b) The p-value for t-test is given by P(t>tstatistic) and the margin of error is given by tcritical*s/n^(1/2). Here s is the sample standard deviation and n is the size of the sample.
Front the given data we can calculate n=64 and s=33.8107. The t-critical value at n-1 I.e. at 64-1=63 degrees of freedom is 1.669. So the margin of error is 1.669*33.8107/(64)^1/2 = 7.568275. So, the correct answer is (c) 7.568275.
(c) The correct option here would be b. The p-value is much greater than 5% this we cannot claim that the averages are different.
(d) Since the confidence interval for the given data is [78.64454, 85.88879] so we can say that we are 95% confident that the mean final grade lies between the values 78.64454 and 85.8879 of students with 8 or more visits to the open lab. So, the option c. We are confident that students with 8 or more visits to open lab sessions have average final grade greater than 78.
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