1. With a normal population distribution and a constant sample size of N = 2, what shape will the sampling distribution of 1000 sample approximate? (1 points)
2. How would you interpret the 99% confidence interval of [5.43,7.83] around a sample mean of 6.44? (2 point)
3. For both of the following density histograms below, compute the approximate area of the shaded region (you may complete your work by hand and include a picture with your answer, if you prefer). (2 point)
Please use R/RStudio to complete the following questions. Include the code you used to generate your answer for each question.
1. Randomly sample 1000 values from both a (a) normal distribution and (b) uniform distribution. Then, check the normality for each. (2 point)
2. Find the mean and 93% and 96% confidence intervals for the normally distributed sample you collected in question 1. (2 points)
a. Do they change when assuming a t-distribution (t-critical)? (2 points)