15. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A simple random sample of pages from a dictionary is obtained. Listed below are the numbers of words defined on those pages. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is the same as the claim that the mean number of defined words on a page is greater than 48.0. Use a 0.10 significance level to test this claim. What does the result suggest about the claim that there are more than 70,000 defined words in the dictionary? 52 36 61 63 45 60 43 42 120 88 What are the hypotheses? O A. Ho: H = 48 OB. Ho: µ = 48 O C. Ho: H = 48 OD Ho: µ > 48 H1:µ < 48 H1: µ > 48 H:µ # 48 H:µ = 48 %3D Identify the test statistic? Identify the P-value? P-value = State the final conclusion that addresses the original claim. Select the appropriate answers. Fail to reject/Reject Ho. There is sufficient/insufficient evidence to support the claim that the mean number of defined words is greater than 48.0 Do the results suggest that there are more than 70,000 defined words in the dictionary? O A. Since many pages that were samples have more than 48 words, there must be more than 70,000 words in the dictionary. O B. There is sufficient evidence to support the claim that there are more than 70,000 words in the dictionary. D C. There is not sufficient evidence to support the claim that there are more than 70,000 words in the dictionary. O D. The results are inconclusive.

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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.