Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the sample mean is 98, the 99% confidence interval to estimate the population mean is
CI99 = mean + or - 2.58(sd/√n)
...where + or - 2.58 represents the 99% confidence interval using a z-table, sd = standard deviation, √ = square root, and n = sample size.
Substitute what you know into the above formula and go from there.
I hope this will help get you started.
To calculate the 99% confidence interval to estimate the population mean, we can use the formula:
CI = x̄ ± (Z * σ/√n)
Where:
CI = Confidence Interval
x̄ = Sample Mean
Z = Z-Score (for a 99% confidence level, Z = 2.576)
σ = Standard Deviation
n = Sample Size
Given:
Sample Mean (x̄) = 98
Standard Deviation (σ) = 12
Sample Size (n) = 36
Z-Score (Z) for 99% confidence level = 2.576
Now, let's substitute the values into the formula to calculate the confidence interval:
CI = 98 ± (2.576 * 12/√36)
First, let's calculate the standard error (σ/√n):
Standard Error = 12/√36 = 12/6 = 2
Now, substitute the values back into the formula:
CI = 98 ± (2.576 * 2)
Next, calculate the upper and lower bounds of the confidence interval:
Upper Bound = 98 + (2.576 * 2) = 98 + 5.152 = 103.152
Lower Bound = 98 - (2.576 * 2) = 98 - 5.152 = 92.848
Therefore, the 99% confidence interval to estimate the population mean is (92.848, 103.152).
To calculate the confidence interval to estimate the population mean, we need to use the formula:
Confidence Interval = Sample Mean ± (Critical Value * (Standard Deviation / √(Sample Size)))
First, we need to find the critical value corresponding to a 99% confidence level. The critical value can be obtained from the standard normal distribution table or a statistical calculator. For a 99% confidence level, the critical value is approximately 2.576.
Next, we substitute the values we have into the formula:
Confidence Interval = 98 ± (2.576 * (12 / √36))
Simplifying this equation:
Confidence Interval = 98 ± (2.576 * 2)
Calculating further:
Confidence Interval = 98 ± 5.152
The confidence interval will be:
Lower Limit = 98 - 5.152 = 92.848
Upper Limit = 98 + 5.152 = 103.152
Therefore, the 99% confidence interval to estimate the population mean is approximately 92.848 to 103.152.