Dawn is a brand of dishwashing liquid owned by Procter & Gamble. Introduced in 1973, it is the best-selling brand of dishwashing liquid in the United States. One of the inactive ingredients in Dawn is sodium lauryl sulfate. If the detergent contains too much of this ingredient, it will not perform as intended. The production process is set so that each bottle of Dawn detergent contains, on average, 8% sodium lauryl sulfate. How many bottles of Dawn detergent should be sampled if the Procter & Gamble quality control engineer wants to be 96% certain of being within 3% of the true population proportion of sodium lauryl sulfate in bottles of Dawn? Answer: n = bottles of Dawn should be sampled
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.
Dawn is a brand of dishwashing liquid owned by Procter & Gamble. Introduced in 1973, it is the best-selling brand of dishwashing liquid in the United States. One of the inactive ingredients in Dawn is sodium lauryl sulfate. If the detergent contains too much of this ingredient, it will not perform as intended. The production process is set so that each bottle of Dawn detergent contains, on average, 8% sodium lauryl sulfate. How many bottles of Dawn detergent should be sampled if the Procter & Gamble quality control engineer wants to be 96% certain of being within 3% of the true population proportion of sodium lauryl sulfate in bottles of Dawn?
Answer: n = bottles of Dawn should be sampled
Solution:
The formula for the sample size is as follows:
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