What is a 95% confidence interval for the time my colleagues can stay awake on average for all of my colleaguesWhat is a 95% confidence interval for the time my colleagues can stay awake on average for all of my colleagues

n=10sample
mean = 2.33
not sure what to do after that

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (±.025) and its Z score.

95% = mean ± Z(SEm)

SEm = SD/√n

Need value of SD.

To calculate the 95% confidence interval for the average time your colleagues can stay awake, you can follow these steps:

Step 1: Determine the sample size (n), which in your case is 10.

Step 2: Find the sample mean (x̄), which is given as 2.33.

Step 3: Identify the standard deviation (σ) of the sample. If you have it, you can use it directly. If not, you can estimate it using the sample standard deviation (s).

Step 4: Calculate the standard error (SE), which is the standard deviation divided by the square root of the sample size. The formula is SE = σ/√n.

Step 5: Determine the critical value from the t-distribution table for a 95% confidence level. Since n is small (n < 30), we use t-distribution instead of the standard normal distribution. For a 95% confidence level and 9 degrees of freedom (n-1), the critical value is 2.262.

Step 6: Calculate the margin of error (ME), which is the critical value multiplied by the standard error. The formula is ME = t * SE.

Step 7: Finally, calculate the upper and lower bounds of the confidence interval (CI) by subtracting and adding the margin of error to the sample mean. The formula is CI = x̄ ± ME.

In your case, the calculations would look like:

SE = σ/√n
CI = x̄ ± t * SE

Since you didn't provide the standard deviation or any additional information, it is challenging to give you the exact confidence interval without those values. Please update your question with the necessary data points, and I will be happy to assist you further.