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
90 15 100 90%
What is the lower bound of the confidence interval?
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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
90 15 100 90%
What is the lower bound of the confidence interval?
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To find the lower bound of the confidence interval, we need to use the formula:
Lower Bound = Mean - (Z-score x Standard Error)
where:
Mean is the sample mean
Standard deviation is the population standard deviation
Sample Size is the sample size
Confidence Level is the desired level of confidence
Z-score is the corresponding value from the standard normal distribution
Standard Error is the standard deviation of the sampling distribution of the mean, calculated as Standard Deviation / sqrt(Sample Size)
Given:
Mean = 90
Standard deviation = 15
Sample Size = 100
Confidence Level = 90%
We can find the Z-score corresponding to a 90% confidence level using a standard normal distribution table or calculator. The value is approximately 1.645.
To find the Standard Error, we use the formula:
Standard Error = Standard deviation / sqrt(Sample Size)
Standard Error = 15 / sqrt(100)
Standard Error = 1.5
Now we can substitute the given values into the formula for Lower Bound:
Lower Bound = 90 - (1.645 x 1.5)
Lower Bound = 87.48
Therefore, the lower bound of the 90% confidence interval is 87.48, rounded to 2 decimal places.