I. Direction: Multiple Choice: Choose the letter that corresponds to your answer. If the answer is not among the choices, choose E before the number. 1. A null hypothesis can only be rejected at the 5% significance if and only if A. The null hypothesis does not make sense. B. The alternate hypothesis is wrong at 5% of the time. C. At 95% confidence interval includes the hypothesized value of the parameter. D. A 95% confidence interval does not include the hypothesized value of the parameter. 2. Consider the null hypothesis H,:p = 0.18 indicates that the proportion of fat content of the burgers being sold in the canteen is 18% or less. Which of the following is true about the type I and type II error? A. A type I error occurs when the actual proportion is about 18% or more, but the null hypothesis is rejected. A type II error when the actual proportion is about18% or less but the null hypothesis is rejected. B. A type I error occurs when the actual proportion is about 18% or less, but the null hypothesis is rejected. A type II error occurs when the actual proportion is about 18% or more, but the null hypothesis is accepted. C. A type I error occurs when the actual proportion is about 18% or more, but the null hypothesis is accepted. A type II error occurs when the actual proportion is about 18% or less, but the null hypothesis is rejected. D. A type I error occurs when the actual proportion is about 18%, and the null hypothesis is rejected. A type II error occurs when the actual proportion is about 18% or less, but the null hypothesis is rejected.

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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.