# solution

11) As we have seen, bootstrap distributions are generally symmetric and bell-shaped and centered at the value of the original sample statistic. However, strange things can happen when the sample size is small and there is an outlier present. Create a bootstrap distribution for the standard deviation based on the following data: “`{r,echo=TRUE}library(boot)x=c(8,10,7,12,13,8,10,50)#add code here“` Describe the shape of the distribution. Is it appropriate to construct a confidence interval from this distribution? Explain why the distribution might have the shape it does.
12) For this problem we are going to build our own normality test using the bootstrap. To do so, we first need to know how to extract the bootstrap confidence interval.
We want to build a function called texttt{mynormtest} that takes as input a vector of numbers and either returns “I think the data is normally distributed” or “I don’t think the data is normally distributed”. The general format of a function is as follows: “`{r}myfun = function(x) { result = sum(x) if (result>0) cat(“The sum is positiven”) if (result}#an example runmyfun(rnorm(100))“`
The `R` package texttt{moments} gives us two very useful functions; texttt{skewness} and texttt{kurtosis}. If data is truly normal, it should have a skewness value of 0 and a kurtosis value of 3. Write an R function that conducts a normality test as follows: it takes as input a data set, calculates a bootstrap confidence interval for the skewness, calculates a bootstrap confidence interval for the kurtosis, then sees if 0 is in the skewness interval and 3 is in the kurtosis interval. If so, your routine prints that the data is normally distributed, otherwise your routine should print that the data is not normally distributed. Test your routine on random data from normal (rnorm), uniform (runif), and exponential (rexp) , with sample sizes of n=10,30,70 and 100.
An example code fragment is below:
“`{r}library(moments)mynormtest = function(x){ #find bootstrap CI for skewness of x # find bootstrap CI for kurtosis of x

##### "Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!" ##### Looking for a Similar Assignment? Our Experts can help. Use the coupon code SAVE30 to get your first order at 30% off!

Hi there! Click one of our representatives below and we will get back to you as soon as possible.

Chat with us on WhatsApp