Assignment 5 Confidence intervals
Show all work, when statkey is used, include a screenprint of your output. If you do not include the screenprint it counts as not working the problem.
1: The data for this problem is in ques1.csv in canvas
Download the data to your computer and upload it to statkey, bootstrap confidence intervals for a mean.
- What is the mean of the data
- What is the standard deviation of the data
- Calculate a t interval for the mean
- What is a bootstrap confidence interval for the mean
- If I tell you that the data is Poisson, calculate the confidence interval for lambda using the normal approximation.
- Using the fact that the data is Poisson calculate the confidence interval for the standard deviation.
The data for this is in ques2.csv, There are 10 measurements in the data set from the first sample, with mean 6.8 and variance 12.84. There are 20 measurements from the second data set with mean 10.5 and variance 14.68.
- Construct a confidence interval for the difference of the two means using the method described in class for normal data with different variances.
- Construct a confidence interval for the difference of the two means using the method described in class for normal data with the same variances.
- Construct a bootstrap confidence interval for the difference in means.
- Construct a confidence interval for the difference in means use the normal approximation when we assume both samples are from Poisson distributions.
Suppose
π₯π₯ππ ππ = 1, … , ππ ππππ πππππππ π π π πππ π π π π π π π ππ πππππππππ π ππππππππ π π ππ π π βπ π πππππππ π π π πππ π π π π π ππππππ π€π€πππ π β πππ π πππππππ π ππ 12 π π π₯π₯ππ(β|π₯π₯ππ β ππ|)
What is the maximum likelihood estimate of ππ? Note π π π₯π₯ππ(π§π§) = π π π§π§ HINT what is the derivative with respect to z of |π§π§| when z is positive, when z is negative???
