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 upper 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
75 10 120 90%
What is the upper bound of the confidence interval?
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Answer:
To calculate the upper bound of the confidence interval, we can use the formula for confidence interval:
Upper Bound = Mean + (Critical Value * Standard Deviation / Square Root of Sample Size)
First, we need to determine the critical value for a 90% confidence level. The critical value for a 90% confidence level with a sample size of 120 can be obtained from a standard normal distribution table or a statistical calculator. For a standard normal distribution, the critical value for a 90% confidence level is approximately 1.645.
Plugging in the given values:
Mean = 75
Standard Deviation = 10
Sample Size = 120
Confidence Level = 90%
Critical Value (z-score) = 1.645
Using the formula:
Upper Bound = 75 + (1.645 * 10 / sqrt(120))
Calculating the square root of 120: sqrt(120) = 10.95 (rounded to 2 decimal places)
Plugging in the values:
Upper Bound = 75 + (1.645 * 10 / 10.95)
Calculating the value:
Upper Bound = 75 + 1.4986 (rounded to 4 decimal places)
So, the upper bound of the confidence interval is approximately 76.50 (rounded to 2 decimal places). Therefore, the answer is 76.50. Note that the answer may be rounded differently depending on the specific rounding rules or requirements of the problem or context