The following list is a sampling of the costs of various statistics textbooks used at several colleges. Give the upper confidence limit for a 95% confidence interval estimate for the mean cost of all statistics textbooks.
109.95; 92.00; 96.70; 84.85; 92.60; 84.45; 90.95; 77.00; 75.50
Formula:
CI95 = mean ± 1.96(sd/√n)
You will need to calculate the mean and standard deviation for your data. In the formula, n = sample size.
Once you have what you need, substitute into the formula and determine the confidence interval.
I hope this will help get you started.
28.22
To find the upper confidence limit for a 95% confidence interval estimate for the mean cost of all statistics textbooks, we need to use the formula:
Upper Confidence Limit = Sample Mean + (Critical Value * Standard Error)
Step 1: Calculate the sample mean
Add up all the textbook costs and divide the sum by the number of textbooks:
109.95 + 92.00 + 96.70 + 84.85 + 92.60 + 84.45 + 90.95 + 77.00 + 75.50 = 803.00
Sample Mean = 803.00 / 9 = 89.22
Step 2: Calculate the standard error
The standard error estimates how much the sample mean may differ from the population mean:
Standard Error = Standard Deviation / sqrt(n)
First, calculate the variance by finding the sum of the squared differences between each textbook cost and the sample mean, and dividing by (n-1):
Variance = ((109.95 - 89.22)^2 + (92.00 - 89.22)^2 + (96.70 - 89.22)^2 + (84.85 - 89.22)^2 + (92.60 - 89.22)^2 + (84.45 - 89.22)^2 + (90.95 - 89.22)^2 + (77.00 - 89.22)^2 + (75.50 - 89.22)^2) / (n-1)
Variance = 1468.051 / 8 = 183.5064
Next, take the square root of the variance to get the standard deviation:
Standard Deviation = sqrt(Variance) = sqrt(183.5064) = 13.5521
Now, calculate the standard error:
Standard Error = 13.5521 / sqrt(9) = 4.5174
Step 3: Find the critical value
To calculate the critical value, we need to determine the confidence level and the degrees of freedom. For a 95% confidence level and a sample size of 9, the degrees of freedom are 8. Looking up the critical value in a t-table, the value is approximately 2.306.
Step 4: Calculate the upper confidence limit
Plug the values into the formula:
Upper Confidence Limit = 89.22 + (2.306 * 4.5174) = 104.13
Therefore, the upper confidence limit for a 95% confidence interval estimate for the mean cost of all statistics textbooks is approximately $104.13.