1. (a) A friend of yours heard that you were taking statistics and has presented you with the following table from which he wants you to construct a histogram.
Age Relative Frequency (%)
0-14 28.4
15-44 50.5
45+ 21.1
100.0
Discuss the problems involved in drawing a histogram from this table.
(b) A student receives test scores of 62, 83, and 91. The student's final exam score is 88 and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% of the final grade. What is the student's mean score in the class?
2. You decide to compare the blood glucose levels (in mg/dL) in individuals in the morning before breakfast and again 1 hour after breakfast. You do this to test the idea that blood glucose levels should rise. You take a blood sample of each individual before and after breakfast. The data are shown below. Conduct the appropriate statistical test stating any assumptions.
Blood glucose level
Individual before breakfast after breakfast DIFF
1 100 150 50
2 85 120 35
3 110 170 60
4 120 160 40
5 130 130 0
6 80 160 80
7 90 180 90
3. The Global Leadership MBA program enrolls students directly from undergraduate studies and others after having obtained some work experience. The students with work experience claim that they do better than their peers because of their experience in the business world. However, the students right out of school claim they do better than their peers because they have more recent academic experience.
The Global Leadership MBA program is not interested in which group does better, but simply in determining whether the two groups' performance is the same or not. To test this, the program took a random sample of students' grades (from a central university database). Let μw denote the population means GPA for the students with work experience and let μN denote the population means GPA for students with no work experience. Let x-w and x-N represent the corresponding sample means.
Write down the null hypothesis and alternative hypothesis that were tested in this study, both in words and using the appropriate notation.
Assume that in answer to the last question, you analyze the data from the random sample of students' grades with a two-sample, two-sided t-test (which may or may not be correct), obtaining the following results:
What conclusion do you reach from the above output?
What is the interpretation of the "Difference" value in the table?