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.
a. What is the mean of the data
b. What is the standard deviation of the data
c. Calculate a t interval for the mean
d. What is a bootstrap confidence interval for the mean
e. If I tell you that the data is Poisson, calculate the confidence interval for lambda using the normal approximation.
f. Using the fact that the data is Poisson calculate the confidence interval for the standard deviation.

2. 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.

a. Construct a confidence interval for the difference of the two means using the method described in class for normal data with different variances.

b. Construct a confidence interval for the difference of the two means using the method described in class for normal data with the same variances.

c. Construct a bootstrap confidence interval for the difference in means.

d. Construct a confidence interval for the difference in means use the normal approximation when we assume both samples are from Poisson distributions.

3. Suppose
𝑥𝑥𝑖𝑖 𝑖𝑖 = 1, … , 𝑛𝑛 𝑖𝑖𝑖𝑖 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑠𝑠𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑠𝑠𝑑𝑑𝑖𝑖𝑛𝑛𝑎𝑎 𝑠𝑠𝑎𝑎 𝑠𝑠ℎ𝑠𝑠 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑠𝑠𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑎𝑎𝑛𝑛 𝑤𝑤𝑖𝑖𝑠𝑠ℎ 𝑑𝑑𝑠𝑠𝑛𝑛𝑖𝑖𝑖𝑖𝑠𝑠𝑑𝑑 1
2 𝑠𝑠𝑥𝑥𝑒𝑒(−|𝑥𝑥𝑖𝑖 − 𝜇𝜇|)
What is the maximum likelihood estimate of 𝜇𝜇? Note 𝑠𝑠𝑥𝑥𝑒𝑒(𝑧𝑧) = 𝑠𝑠𝑧𝑧 HINT what is the derivative with respect to z of |𝑧𝑧| when z is positive, when z is negative???