Please provide a step by step solution and explanation.

Confidence Intervals at Work. The goal of a confidence interval is to estimate an unknown parameter. A confidence interval is comprised of an estimate from a sample, the standard error of the statistic and a level of confidence. We choose a confidence level based on how precise we need our estimate to be and how willing we are to risk not obtaining the parameter at all. The definition of a 95% confidence interval states: Out of all possible samples of size n taken from the population, the confidence intervals calculated based on those sampies wiii contain the true parameter value 95% of the time. This means when we perform a 95% confidence interval 5% of all intervals will not contain the true parameter. Therefore, we assume a 5% risk we might get an interval that does not contain the true parameter. We hope we get one of the \"good\" intervals. In practice, we will not know. The simulation repeatedly samples from a population, calculates a confidence interval for each sample and indicates how many confidence intervals obtain the true mean. The goal ofthis simulation is to visualize and validate the definition of a confidence interval. Getting Started: Go to the Simulation in Lesson 22 in the Week 7 Module in Canvas. 1. Start with a 90% confidence interval and the population for standard deviation. 2. Change Sample Size to 15 and "if of Simulations" to 1. 3. This means you are just taking 1 sample of n = 15. This is most similar to what we do in \"the real world\". We only take one sample to estimate a parameter. a. (1 point) Does your 90% confidence interval contain the true mean? b. (1 point) Increase "ll of Simulations" to 1000. Theoretically, 90% of the sample means we obtain should result in an interval that contains the true parameter. Does this seem to be the case? (1 point) What type of sample will fail to capture the true parameter? c Decrease \"if of Simulations\" to 100. The intervals that don't contain the true mean are indicated in red. You can hover over a sample mean (dot in center of interval) to see it's value and the interval's margin of error. a Is there a common feature from the intervals that do not contain the true mean? 0 Where are their sample means with respect to the sample means of the intervals that do contain the parameter? 0 Consider the placement of the sample mean in the sampling distribution. 0 Optional: Perform the previous steps using confidence levels 95% and 99%. (1 point) How does sample size affect your confidence intervals? Continue with a 90% Confidence Level and \"ll of Simulations\" at 100. Choose a smaller sample size between 2 and 10 observe the width of your intervals. Increase the sample size to something between 30 and 100 observe the width of your intervals. Increase your sample size to 1000 observe the width of your intervals. e. (1 point) How does the confidence level affect your confidence intervals? 0 Continue with a 90% Confidence Level, "ll of Simulations\" at 100 and a moderate sample size between 30 and 100. Observe the width of your intervals. 0 Increase the confidence level to 95% observe your intervals. 0 Increase the confidence level to 99% observe your intervals