What is construct a 95 percent confidence interval about the sample mean N= 11?
To construct a 95% confidence interval about the sample mean for a given sample size N = 11, you will need the following information:
1. Sample mean (x̄): This is the average value of your data points in the sample. Let's assume you have already calculated it.
2. Standard deviation (σ) or standard error (SE): The standard deviation measures the variability of the data points in your sample, while the standard error measures the variability of the sample mean. If you have the standard deviation, you can use it directly. If not, you can estimate the standard error using the formula σ/√n, where σ is the population standard deviation (if known) and n is the sample size.
Now, let's calculate the confidence interval step by step:
Step 1: Determine the critical value
To construct a 95% confidence interval, you need to find the critical value from the t-distribution table or use a statistical software. With a sample size of 11, you will have 10 degrees of freedom. For a 95% confidence interval, the critical value will be approximately 2.228 based on the t-distribution.
Step 2: Calculate the margin of error
The margin of error is determined by multiplying the critical value by the standard deviation (or standard error). The formula for the margin of error is:
Margin of error = Critical value * Standard deviation (or Standard error)
Let's assume you have calculated the margin of error.
Step 3: Calculate the lower and upper bounds
The lower bound of the confidence interval is given by:
Lower bound = Sample mean - Margin of error
The upper bound of the confidence interval is given by:
Upper bound = Sample mean + Margin of error
By substituting the values into these formulas, you can calculate the lower and upper bounds of the confidence interval for the sample mean.
Note: The confidence interval is an interval estimate that is likely to contain the true population mean with 95% confidence. It provides a range within which the true population mean is expected to lie based on the information from the sample.
Remember to interpret the confidence interval carefully. For example, you could say: "Based on our sample of size 11, we are 95% confident that the true population mean falls between the lower bound and the upper bound of the confidence interval."