The University of Michigan is interested in determining if the performance of students in Advanced Statistics differs depending on whether students attend only online classes or only face to face. The final grades of 15 students who attend classes solely online was obtained as well as a further 15 students who attend classes face to face. The grades are provided in the table below: Online 86 86 91 68 78 45 93 59 63 75 69 79 82 68 47 Face to Face 50 80 52 92 90 91 72 76 85 44 50 44 57 93 65 Construct a box and whisker plot for: (i) online classes and (ii) face to face classes. Test, at the 5% significance level, whether there is a difference in the mean grades of the two class types. C. Confirm test results in part (b) using JASP. Note: All JASP input files and output tables should be provided
The University of Michigan is interested in determining if the performance of students in Advanced Statistics differs depending on whether students attend only online classes or only face to face. The final grades of 15 students who attend classes solely online was obtained as well as a further 15 students who attend classes face to face. The grades are provided in the table below: Online 86 86 91 68 78 45 93 59 63 75 69 79 82 68 47 Face to Face 50 80 52 92 90 91 72 76 85 44 50 44 57 93 65 Construct a box and whisker plot for: (i) online classes and (ii) face to face classes. Test, at the 5% significance level, whether there is a difference in the mean grades of the two class types. C. Confirm test results in part (b) using JASP. Note: All JASP input files and output tables should be provided
The University of Michigan is interested in determining if the performance of students in Advanced Statistics differs depending on whether students attend only online classes or only face to face. The final grades of 15 students who attend classes solely online was obtained as well as a further 15 students who attend classes face to face. The grades are provided in the table below: Online 86 86 91 68 78 45 93 59 63 75 69 79 82 68 47 Face to Face 50 80 52 92 90 91 72 76 85 44 50 44 57 93 65 Construct a box and whisker plot for: (i) online classes and (ii) face to face classes. Test, at the 5% significance level, whether there is a difference in the mean grades of the two class types. C. Confirm test results in part (b) using JASP. Note: All JASP input files and output tables should be provided
The University of Michigan is interested in determining if the performance of students in Advanced Statistics differs depending on whether students attend only online classes or only face to face. The final grades of 15 students who attend classes solely online was obtained as well as a further 15 students who attend classes face to face. The grades are provided in the table below:
Online
86
86
91
68 78 45
93
59 63
75 69 79 82
68
47
Face to Face
50
80
52 92 90 91 72 76 85
44 50 44 57 93 65
Construct a box and whisker plot for: (i) online classes and (ii) face to face classes.
Test, at the 5% significance level, whether there is a difference in the mean grades of the two class types.
C.
Confirm test results in part (b) using JASP. Note: All JASP input files and output tables should be provided
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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A researcher is interested in measuring the memory recall of students. Twenty students were given fifteen minutes to try to memorize a list of 15 phrases. Each student was then asked to list as many of the phrases as he or she could remember both two hours and twenty-four hours later. The number of phrases recalled correctly for each student are shown below. Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Two Hours 7 1 9 13 3 0 3 14 0 12 2 2 12 10 2 4 3 11 5 4 Twenty-Four Hours 2 2 4 14 10 9 4 3 1 3 14 4 1 0 11 10 10 12 14 13 a. Calculate the following for each group: i. 20% trimmed mean ii. The interquartile range b. Test the hypothesis that the mean for the memory after two hours is less than 5. Use the 1% level of significance. c. Determine whether there is evidence, at the 5% level of significance, that for all students, the mean number of words recalled after two hours exceeds that recalled after twenty-four hours. d. Confirm test results in part (c) using JASP.
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