Final answer:
To estimate with 94% confidence the mean winnings for Jeopardy players, one must calculate the confidence interval by finding the sample mean, the sample standard deviation, the critical t-value, and then computing the margin of error to add and subtract from the sample mean for the UCL and LCL.
Step-by-step explanation:
To estimate the mean winnings for all Jeopardy show's players with a 94% confidence level, one needs to calculate the confidence interval using the sample data given. The formula for confidence interval is mean ± (critical value * standard error), where the critical value is determined from the t-distribution with n-1 degrees of freedom because the population standard deviation is unknown. Since your question does not provide a table or calculator for t-scores, I will describe the steps without actual calculations:
- Calculate the sample mean (average) of the winnings.
- Calculate the sample standard deviation.
- Find the t-score for 94% confidence and degrees of freedom (n-1), where n is the number of samples.
- Calculate the standard error by dividing the standard deviation by the square root of n.
- Multiply the t-score by the standard error to get the margin of error.
- Finally, add and subtract the margin of error from the sample mean to get the Upper Confidence Limit (UCL) and Lower Confidence Limit (LCL) respectively.
Once these calculations are performed, you would obtain the estimated mean winnings range for all Jeopardy players at a 94% confidence level.