Question

The following is a multi-part problem, report the r code used for the following

1. Obtain 854 values at random from a uniform distribution where the smallest possible value is 10 and largest is 30. name the vector ex2. Consider ex2 the population.

2. Generate a histogram of ex2

3. Randomly obtain 7 samples with 10 observations in each sample from ex2 using sampling with replacement. Name the vector sam7. Calculate the mean for each sample and name that object sammean7.

4.Randomly obtain 70 samples with 10 observations in each sample from ex2 using sampling with replacement. Name the vector sam70. Calculate the mean for each sample and name that object sammean70.

5. Calculate the mean and standard deviation of ex2, sam7, sam70

6. Which sample has estimates closer to the corresponding parameter (true population mean).

Answer 1

a) and b) The above R commands generates 854 random values from Uniform Distribution with min value as 10 and max value as 30 using the command runif. The vector is stored in ex2 and the histogram is made using the command hist in R and the graph shows the uniform distribution.

c) sammean is a function that has been created in R, in this function just pass the argument as number of sample required and it will calculate the mean of those many samples with 10 observations each. Hence, the mean for 7 samples of 10 observations each from uniform distribution is 20.20 as shown above.

d) Similarly, just changing the value to 70 in the argument of the function sammean will give the mean os 70 samples of 10 observations each which is equal to 20.18

e) Similarly, we have the function which calculates standard deviation in a similar way as mean

So, samsd is the function which will calculate the standard deviation for 7 samples or 70 samples, shown below

mean(ex2) = 19.90

mean(sam7)= 19.42

mean(sam70) = 19.87

Also, for standard deviation,

sd(ex2) = 5.75

sd(sam7)= 5.59

sd(sam70)= 5.66

From mean and standard deviation, we see that the mean and standard deviation of 70 samples is more close to the true population mean and standard deviation.