Question

(Q5.1) Consider the samples {1, 2, 3, 4, 5, 6}. Using a random number generator, obtain three different bootstrap samples and their respective means. What is the bootstrap estimate of the standard error of the sample mean using these three replicates?

Answer #1

**IN R**

Firstly let us feed in the data:

**dat <- c{1,2,3,4,5,6}**

Generate 3 bootstrap replications and their respective means:

**n <- length(dat)** *#n=6*

**B <- 3**

**boot <- numeric(B)**

**for (i in 1:B) { idx <- sample(1:n, size = n, replace
= TRUE)** *#choose 8 indices with replacement*

**boot[i] <- mean(sort(dat[idx])[3:6])**
*#draw sample, compute & store trimmed mean*

**}**

Compute bootstrap estimate of standard error:

**se <- sd(boot)**

**cat("Bootstrap estimate of standard error is",
se)**

Consider the samples f1; 2; 3; 4; 5; 6g. Using a random number
generator,
obtain three different bootstrap samples and their respective
means. What is the bootstrap estimate
of the standard error of the sample mean using these three
replicates?
Written not in R

The following two samples were collected as matched pairs: Pair
1 2 3 4 5 6 7 8 Sample 1 8 4 6 9 9 7 9 8 Sample 2 5 7 6 5 6 9 7 6
a. State the null and alternative hypotheses to estimate the
difference in means between the populations from which Samples 1
and 2 were drawn. b. Calculate the appropriate test statistic and
interpret the results of the hypothesis test using α = 0.1....

Assume that a population of size 5 specifies that all possible
samples of size "3" are extracted without repetition.
Values:
2,500.00
2,650.00
2,790.00
3,125.00
3,200.00
1) Calculate the mean and standard deviation of the
population.
2) Calculate all possible samples, their means and standard
deviations.
3) Calculate the standard error of the means using the standard
deviations.
4) Show that the expected value of the sample mean is equal to
the mean of the population.
5) Show that the expected...

Consider the following sample: 1, 5, 5, 3, 4, 3, 6, 4, 1, a
1) If the mean of this numerical data set is 3.7 , find the
value of a
2) Evaluate the standard deviation the sample
3) Find P80

2) Airline accidents: According to the U.S. National
Transportation Safety Board, the number of airline accidents by
year from 1983 to 2006 were 23, 16, 21, 24, 34, 30, 28, 24, 26, 18,
23, 23, 36, 37, 49, 50, 51, 56, 46, 41, 54, 30, 40, and 31.
a. For the sample data, compute the mean and its standard error
(from the standard deviation), and the median.
b. Using R, compute bootstrap estimates of the mean, median and
25% trimmed...

Question 6. Using only a random number
generator that simulates a random number between [0,1], simulate
1,000 iterations of the following random variables:
a) X ~ exp(5)
b) X such that f(x) = 3x2 , 0 ≤ x ≤ 1
For both (a) and (b), plot a histogram of your simulated random
variable. Estimate ?̅ and s2. Compare these values to E(X) and
Var(X).

5. The number of defects in 4 different samples of 80 units
coming off of a production line are as follows: {1, 2, 4, 5}
If I took samples of size 2 from this list, with replacement,
there are 16 different permutations.
List them below:
Find the mean of each sample, then create a table showing the
sampling distributions of the sample means.
Find the mean of the sampling distribution.
Find the mean of the 4 data values. What do...

Consider the following time series
data.
Week
1
2
3
4
5
6
Value
18
14
16
12
17
14
Using the naive method (most recent value) as the forecast for
the next week, compute the following measures of forecast accuracy.
Round the intermediate calculations to two decimal places.
Mean absolute error (to 1 decimal).
Mean squared error (to 1 decimal).
Mean absolute percentage error (to 2 decimals).
%
What is the forecast for week 7 (to the nearest whole...

Consider the following dependent random samples
Observations 1
2 3
4 5
6
x-values
22.0 21.0
18.1 19.6 13.2
17.5
y-values
23.1 21.7
18.7 20.7
14.7 16.4
a) Determine the difference between each set of points,
xi - yi
b) Do hypothesis testing to see if µd < 0 at the α
= .05.

Consider the following time series data.
Week
1
2
3
4
5
6
Value
19
14
16
11
18
15
Using the naive method (most recent value) as the forecast for
the next week, compute the following measures of forecast accuracy.
Round the intermediate calculations to two decimal places.
Mean absolute error (to 1 decimal).
Mean squared error (to 1 decimal).
Mean absolute percentage error (to 2 decimals).
%
What is the forecast for week 7 (to the nearest whole...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 6 minutes ago

asked 13 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 23 minutes ago

asked 34 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago