Question

researchers plan to take another sample of whale and cruise ship encounters in the west arm sub-region of glacier bay. assuming , if the researchers would like to ensure that the standard deviation of the sample proportion is no larger than 0.03, how many encounters would they need to include in their sample? round your answer to the nearest whole number.

Answer 1

To determine the minimum number of encounters researchers would need to include in their sample, use the formula n = (Z×σ/E)² with the given values. In this case, the researchers would need to include 4 encounters in their sample.

Step-by-step explanation:

To determine the minimum number of encounters the researchers would need to include in their sample, we can use the formula:

n = (Z×σ/E)²

Where:

n is the sample size

Z is the z-score that corresponds to the desired level of confidence (e.g., for 95% confidence, Z = 1.96)

σ is the standard deviation of the population proportion

E is the desired margin of error

In this case, the researchers want the standard deviation of the sample proportion to be no larger than 0.03. Therefore, σ = 0.03. Let's assume they want a 95% confidence level (Z = 1.96) and a margin of error of 0.03 (E = 0.03).

Plugging these values into the formula, we get:

n = (1.96×0.03/0.03)²

n = 1.92²

n ≈ 3.69

Rounding to the nearest whole number, the researchers would need to include 4 encounters in their sample.

Answer 2

To ensure that the standard deviation of the sample proportion is no larger than 0.03, the researchers would need to include 1079 encounters in their sample.

Step-by-step explanation:

To determine the minimum number of encounters the researchers would need to include in their sample, we need to use the formula:

n = (Z * σ / E)²

where 'n' is the sample size, 'Z' is the z-score corresponding to the desired level of confidence, 'σ' is the standard deviation of the population, and 'E' is the maximum acceptable margin of error.

In this case, the researchers want the standard deviation of the sample proportion to be no larger than 0.03. So, we can use a conservative estimate of the standard deviation of the population proportion as 0.5.

Assuming a 95% confidence level, the corresponding z-score is approximately 1.96. Plugging these values into the formula, we get:

n = (1.96 * 0.5 / 0.03)² ≈ 1078.22

Rounding up to the nearest whole number, the researchers would need to include 1079 encounters in their sample.