Question

A company is market testing a new flavor of coffee. The developers of the flavor estimated that 64% of consumers will like the new drink. A sample of 130 consumers was recruited to taste test the new drink. Determine the standard error of the proportion.

Answer 1

The standard error of the proportion is calculated using the formula sqrt[p(1-p)/n]. For an estimated proportion of 0.64 (64%) and a sample size of 130 consumers, the standard error would be approximately 0.0421.

Step-by-step explanation:

To determine the standard error of the proportion, you would use the formula for the standard error of a sample proportion, which is sqrt[p(1-p)/n], where p is the estimated proportion of consumers who will like the new drink, and n is the sample size. In this case, the estimated proportion is 0.64 and the sample size is 130 consumers.

Therefore, the standard error of the proportion would be calculated as follows:

Standard Error = sqrt[0.64(1-0.64)/130]

Standard Error = sqrt[0.64*0.36/130]

Standard Error = sqrt[0.2304/130]

Standard Error = sqrt[0.001773]

Standard Error ≈ 0.0421

The standard error of the estimated proportion of consumers who like the new coffee flavor is approximately 0.0421.