In a large Midwestern university an SRS of 100 entering freshmen in 2014 found that 20 finished in the bottom third of their high school class. In 2016, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. In both years, the entering freshman class had roughly 6000 students. Let p, be the proportion of all entering freshmen in 2014 who graduated in the bottom third of their high school class and let p, be the proportion of all entering freshmen in 2016 who graduated in the bottom third of their high school class. Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2016 has been reduced, compared to the proportion in 2014? You test the hypotheses Ho:P1 - P2 = 0; Ha: p, - P2 > 0, using a = 0.05. The test statistic is 1.980. Which of the following is the appropriate P-value and conclusion for your test. P-value = 0.047; fail to reject H; we do not have convincing evidence that the proportion who %3D graduated in the bottom third of their class has been reduced. P-value = 0.047; accept H,; there is convincing evidence that the proportion who graduated in the bottom third of their class has been reduced. P-value = 0.024; fail to reject H,; we do not have convincing evidence that the proportion who graduated in the bottom third of their class has been reduced. P-value = 0.024; reject H, ; we have convincing evidence that the proportion who graduated in the bottom third of their class has been reduced. P-value = 0.024; fail to reject Ho; we have convincing evidence that the proportion who graduated in the bottom third of their class has not changed.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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