The standard deviation of 100 random samples of the same size is approximated to be 0.98. What is the margin of error?
Answer (2)
Use the formula: M a r g in o f E rror = z ∗ ( s t an d a r dd e v ia t i o n / s q r t ( n u mb ero f s am pl es )) .
With a 95% confidence level, z ≈ 1.96 .
Plug in the values: M a r g in o f E rror = 1.96 ∗ ( 0.98/ s q r t ( 100 )) .
Calculate the margin of error: M a r g in o f E rror = 0.19208 .
Explanation
Understand the problem and provided data We are given the standard deviation of 100 random samples, which is approximately 0.98. Our goal is to find the margin of error.
State the formula for margin of error The formula for the margin of error is given by: M a r g in o f E rror = z × N u mb er o f S am pl es St an d a r d De v ia t i o n where z is the z-score corresponding to the desired confidence level.
Identify the z-score and given values For a 95% confidence level, the z-score is approximately 1.96. We are given the standard deviation as 0.98 and the number of samples as 100.
Calculate the margin of error Plugging in the values, we get: M a r g in o f E rror = 1.96 × 100 0.98 M a r g in o f E rror = 1.96 × 10 0.98 M a r g in o f E rror = 1.96 × 0.098 M a r g in o f E rror = 0.19208
State the final answer Therefore, the margin of error is approximately 0.19208.
Examples
In polling, the margin of error indicates how much the results of a survey might differ from the true population value. For example, if a poll finds that 60% of people support a candidate with a margin of error of 5%, the true percentage of support in the population is likely between 55% and 65%. This helps to understand the reliability of the survey results and make informed decisions based on the data.
The margin of error for 100 samples with a standard deviation of 0.98 is calculated to be approximately 0.19208 using the formula that includes the z-score for a 95% confidence level. This formula accounts for the number of samples and provides a reliable estimate of the error range for the data. Thus, the margin of error indicates the potential variation from the true population value based on the sample data.
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