# inference

1. ### Help required with statistics course

Hi, I need to complete a statistics course to complete my degree but I am struggling with it quite a bit. I have attempted some of the questions on my current assignment but overall I'm not sure how to go about it at all. I was wondering would anyone be able to help me to understand how to do...
2. ### Interpreting Results of Monte Carlo Simulation (R)

Hello, I have conducted a Monte Carlo simulation in R based on the guidelines below and I am struggling to interpret my results. Consider the following data-generating process Y = β1 × X + u 1. Simulate 1000 samples of size n = 100 with β1 = 2, X ∼ N(100,15) and u ∼ N(0,8). 2. In each...
3. ### Can this problem be modeled?

I have a question about whether I can model in a way that solves this problem: Suppose a swimming coach has 100 athletes and only cares about the distance they can each swim in 5 minutes. From this, he sets a baseline expectation of each swimmer’s "5-minute distance" expectation that is...
4. ### Inference Statistic - Likelihood Function

## LaTeX Code Can anyone help me understand this? Consider the four observations from de Normal Distribution with variance equal to one $y_1 < 10$$, y_2 > 10$, $5 < y_3 < 10$ and $y_4 = 10$. The likelihood function is? Would be: \$ \prod_{1}^{4} \frac{1}{\sqrt(2\pi)}\exp{-\frac{(y_i...
5. ### Relative Efficiency

Consider the following equation: T_i = A_i + Z_i * B_i,i=1,2...,6. Suppose for all i(i=1,2,...,6) data generation of A_i and B_i are exactly same for two methods. The two methods differ only in generating data of Z_i. For method 1, Z_i is generated from Bernoulli distribution with...
6. ### Checking significance of bias.

In a new design, estimator seems to be biased but efficient than the existing design. Now I want to check whether the bias of the estimator based on new design is significant. The formula of the variance of the estimator based on new design is intractable. How can I check the...
7. ### Parametric vs. Nonparametric.

Suppose a researcher estimated a parameter in parametric way with correct distributional assumption. Another researcher estimated the same parameter in non-parametric way. Will there any difference of accuracy (bias) in estimation in these two situations?
8. ### What are these formulas and what is their purpose? n=(sigma^2)(Z_alpha/h^2); two more

I can't find reference to these formulas in the slides posted by my professor. I also can't find any versions of these formulas anywhere else online - guess my google-fu sucks. I get what Z_alpha is (critical value), I know what sigma is (population standard deviation), and n I guess is the...
9. ### Assumption for inferential regression

I was reading about regressional inference and one of the assumptions stated was: The standard deviation of the responses about the population line is the same for all values of the explanatory variable. I understand this as: If X has a certain value the mean value of Y for that X...
10. ### Statistical inference

Hi there, I would like to ask a couple of basic questions: 1. What is the difference between estimation and hypothesis testing? I mean are they two options for inference? or estimation of the parameters comes first and then we apply the hypothesis testing? 2. How can I determine what is...
11. ### URGENT: What are the statistical limits and biases in this scientific article?

I need to deliver this exercise in the next 10 hours. QUESTION: What are the statistical limits and biases in this scientific article, which challenge its validity? THE ARTICLE: Efficacy of hepatitis A vaccine in prevention of secondary hepatitis A infection: a randomised trial Abstract...
12. ### Does Imposing a Constrain Make a Method More Powerful?

Suppose we have 100 patients in a randomized trial. 50 of them are in treatment group and the rest are in placebo group. This is a longitudinal study so that we measure the response from each individual at four different periods: baseline, week 1, week 4, and week 6. Now suppose we have good...
13. ### Composite Hypothesis Testing Problem

Hello guys, So I have this problem I am trying to solve and its
14. ### Test to compare difference between median value in two discrete samples

Hi, I have two collection of ordinal samples for a discrete variable related to two administration of an experiment. Using Kolmogorov-Smirnov, I checked that I can't reject the Ho Hypothesis that the two distribution are the same. Now I would like to check if the median of these two collection...
15. ### proportion inference analysis

Hi. I have data on 1027 potential donors to a non-profit organization. I want to see if our online ads have impacted their donation rates. The people who sent me the data have a record for each of the 1027. They included a "sample weight" column which indexes the demographics columns. So...
16. ### Finding a UMVUE for variance of normal distribution

Let Let X_1,X_2,...,X_n be a random sample from a normal distribution with mean \mu and variance \sigma^2 . I showed that (\bar X,S^2) is jointly sufficient for estimating ( \mu , \sigma^2 ) where \bar X is the sample mean and S^2 is the sample variance. Then assuming that (\bar...
17. ### Inference using simulated quantile function

I generated a quantile function \hat X using Monte Carlo simulation. The random variable I simulate is the mean value of 5 draws from an i.i.d. range statistic Y. I.e., I have Y(\sigma) \sim \sigma F(), and I simulated the value of X(\sigma=1) \sim \sum_{1}^{5} y(1)_i / 5. Is it valid for...
18. ### Probability and Sampling distribution

Would you please explain me the difference between *Probability distribution and Sampling distribution* easily ? Is that the difference : in probability distribution we have probability for every individual whereas in sampling distribution we get probability for statistic ? Does sampling...
19. ### Computing sample size and Best Critical Region

Let X_1,X_2,\ldots,X_n denote a random sample from a normal distribution N(\theta,100). Show that C=[(x_1,x_2,\ldots,x_n):c\leq \bar x=\frac{\sum_1^n x_i}{n}] is a best critical region for testing H_o:\theta=75 against H_1:\theta=78. Find n and c so that...
20. ### Unbiased Estimator.

the radius of a circle is measured with an error of measurement which is distributed normal with mean 0 and variance \sigma^2,\sigma^2 unknown.Given n independent measurements of the radius , find an unbiased estimator of the area of the circle. By using *Maximum Likelihood Estimator* I found...