Calculate for the following given the values below. Express your answer in 2 decimal places (example: 25.00)
Mean Standard deviation Sample Size Confidence Level
75 10 120 90%
What is the margin of error?
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Calculate for the following given the values below. Express your answer in 2 decimal places (example: 25.00)
Mean Standard deviation Sample Size Confidence Level
75 10 120 90%
What is the margin of error?
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Answer:
To find the margin of error, we need to first calculate the critical value for the given confidence level of 90%. We can find this value using a t-distribution table and the sample size of 120.
For a 90% confidence level and 119 degrees of freedom (since we have a sample size of 120), the critical value is approximately 1.645.
Next, we can use the formula for margin of error:
Margin of Error = Critical Value x Standard Error
where the standard error is the standard deviation divided by the square root of the sample size:
Standard Error = Standard Deviation / sqrt(Sample Size)
Plugging in the values we have:
Standard Error = 10 / sqrt(120) =
The margin of error can be calculated using the following formula:
Margin of error = Z * (standard deviation / sqrt(sample size))
Where Z is the z-score corresponding to the desired confidence level.
For a 90% confidence level, the z-score is 1.645.
Plugging in the values given:
Margin of error = 1.645 * (10 / sqrt(120))
= 1.645 * (10 / 10.954)
= 1.645 * 0.912
= 1.50 (rounded to 2 decimal places)
Therefore, the margin of error is 1.50.