Discussion Question 2: Why check for normality? In Section 6.2-D, you learn that if the sample is small (less than 20) and the data contain clear outliers or skewness, then we should avoid using the t-distribution. In this Discussion Question, we will see why this is necessary as we work through a condence interval example. We will start with a a skewed distribution to be our population distribution, called the exponential distribution. The exponential distribution has one parameter ,u that determines both the mean and the standard deviation of the distribution. Below is the graph of the exponential distribution with n = 1, and the standard deviation 0' = ,u = 1. It is clearly heavily skewed to the right. 1.0 0.8 0.6 0.4 0.2 0.0 1'15 ,u-srxi-I n-So{X}-I ai-vmm-I (1) Use the same applet as in the last discussion question, under method, choose means, exponential, t. Pick your favorite ,u (must be positive), in = 5, and intervals 10000. Use condence level 95%. Hit \"Sample\". What is the percentage of the intervals containing ,u? (Include a screenshot) (2) Now change the n = 20, n = 50, n = 100 and repeat the last part. (Include screenshots) What pattern do you see for the coverage success rate as 11 gets larger? Why is that? Now let us change our population distribution from the exponential distribution to uniform distribution. The graph of the uniform distribution is a horizontal line with two parameters a and b. a is where the 1 ba distribution starts and b is where the distribution ends. The uniform distribution has mean and 5-65 2~/' is 1/ 3 and the standard deviation 0' = ?3' It is clearly a symmetric distribution and not skewed at all. standard deviation Below is the graph of the uniform distribution with a = 1 and b = 4. The mean ACTIVITIES AND ASSIGNMENTS FOR WEEK 7 3 [3) Use the same applet as in the last discussion question, under method, choose means, uniform, t. Choose your favorite :1 and I) (must be a.