Nassau Community College uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 848 hours with a population standard deviation of 72 hours. A manufacturer claims that its new brand of bulbs, which cost the same as the brand the college currently uses, has a mean life of more than 848 hours. The college has decided to purchase the new brand if, when tested, the test evidence supports the manufacturer's claim at the 1% significance level. Suppose 49 bulbs were tested and the mean life was found to be 866. Complete the steps of a hypothesis test below, and then answer the question, "should the college purchase the new brand of light bulbs?" (a) State the hypotheses: Ho: The Select an answer v light bulb life Select an answer hours. Symbols: u ? v Ha: The Select an answer v light bulb life Select an answer hours. Symbols: Hp - I2 (b) The correct symbol for the mean of the sampling distribution is: P1-P2 (c) The value for the mean of the sampling distribution is:

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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.