Homework 8

CHE 116: Numerical Methods and Statistics

3/22/2018

1.CLT Concepts (8 Points)

1. If you sum together 20 numbers sampled from a binomial distribution and 10 from a Poisson distribution, how is your sum distribted?

2. If you sample 25 numbers from different beta distributions, how will each of the numbers be distributed?

3. Assume a HW grade is determined as the average of 3 HW assignments. How is the HW grade distributed?

4. You measure the height of 3 people. What distribution will the uncertainty of the mean of the heights follow?

2. Confidence Interval (16 Points)

Report the given confidence interval for error in the mean using the data in the next cell and describe in words what the confidence interval is for each example. 4 points each

1. 80% Double.
2. 99% Upper ( a value such that the mean lies above that value 99% of the time)
3. 95% Double
4. Redo part 3 with a known standard deviation of 2

data_1 = [0.41,2.69,3.82,0.42,1.20]

data_2 = [5.07,2.79,1.24,6.50,3.17,3.59,5.42,4.10,1.26,0.54,1.22,4.43,3.83,0.93,3.45,5.24,3.51,4.64,0.65,3.27,2.41,4.31,4.15,2.24,2.30,3.3]

data_3 = [5.62,2.34,2.76,2.80,1.15,5.19,-0.91]

Confidence Intervals (8 Points)

State what distribution and its parameters for each of the following cases. 2 points each.

1. $P(\mu - \bar{x})$, $\sigma = 2.4$, $N = 4$
2. $P(\mu)$, $\bar{x} = 11$, $\sigma_x = 3.2$, $N = 11$
3. $P(\mu)$, $\bar{x} = -3$, $\sigma_x = 2.1$, $N = 35$
4. $P(\mu)$, $\bar{x} = 6$, $\sigma = 11$, $N = 30$