A random sample of 40 binomial trials resulted in 16 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the p distribution? Explain. O Yes, n-p and n-g are both greater than 5. O No, n-q is greater than 5, but n-p is less than 5. O No, n-p and n-g are both less than 5. O No, n-p is greater than 5, but n-g is less than 5. O Yes, n-p and n-q are both less than 5. (b) State the hypotheses. O Ho: p < 0.5; H :D = 0.5 O Hoip = 0.5; H,:p < 0.5 • Hgi p = 0.5; H,: p ± 0.5 O Hg:p = 0.5; H,: p > 0.5 (c) Compute p. (Enter a number.) .4 Compute the corresponding standardized sample test statistic. (Enter a number. Round your answer to two decimal places.) |-1.26 (d) Find the P-value of the test statistic. (Enter a number. Round your answer to four decimal places.) 1038

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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.