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

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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

Expert Solution
Step 1

Solution:

The formula for the sample size is as follows:

Z.
n= p(1-p)|
a/2
Here, za2 is the critical value at 96% confidence level, pis the population proportion and E is the
margin of error.
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