Question 7
We know that a sample statistic is used to infer about a parameter of the population; a statistic is said to be an unbiased estimator of the parameter, if the mean of the sampling distribution for the statistic is same as the population parameter.
Therefore, the complete statement is
A sample statistic is an UNBIASED estimator of the population parameter, if the mean of the sampling distribution for the sample statistic is the POPULATION PARAMETER.
Question 8
A distribution has a mean of 12 and a variance of 250.
If X denotes the population, then
Now, we have to find the second moment about the origin for X.
So, basically we have to find
Now, according to the definition of Variance of X,
So, the answer is
The second moment about the origin is 394.
Please answer all parts. 7. A sample statistic is an estimator of the population parameter, if...
1. Select all true statements about sample mean and sample median. A) When the population distribution is skewed, sample mean is biased but sample median is an unbiased estimator of population mean. B) When the population distribution is symmetric, both mean and sample median are unbiased estimators of population mean. C) Sampling distribution of sample mean has a smaller standard error than sample median when population distribution is normal. D) Both mean and median are unbiased estimators of population mean...
QUESTION 10 What is the difference between a parameter and a statistic? O Parameters are sample values and statistics are population values. O None of the above. O Parameters are population values and statistics are sample values. O Parameters and statistics are both sample values. There is no difference between them. O Parameters and statistics are both population values. There is no difference between them. QUESTION 11 What is the sampling distribution of a statistic? O The distribution of statistic...
An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated. true or false?
please answer correctly and answer all questions.. this is revision question... 7. Which of the following is BEST graphical method for describing categorical data? A. Bar chart B. Histogram C.Box-plot D. Pareto chart 8. Which of the following is NOT property of the variance? A. It measures the amount of spread or variability of observation from mean B. Standard deviation is square root of variance C. Normally used for describing measure of dispersion during reporting research data D. It is...
Please answer the question clearly. Consider a random sample of size n from a Poisson population with parameter λ (a) Find the method of moments estimator for λ. (b) Find the maximum likelihood estimator for λ. Suppose X has a Poisson distribution and the prior distribution for its parameter A is a gamma distribution with parameters and β. (a) Show that the posterior distribution of A given X-x is a gamma distribution with parameters a +r and (b) Find the...
Complete the sentence: An unbiased estimator is _____. a. any sample statistic used to approximate a population parameter b. a sample statistic, which has an expected value equal to the value of the population parameter c. a sample statistic whose value is usually less than the value of the population parameter d. any estimator whose standard error is relatively small
please do all parts and be neat. i will give good rating! It is estimated that the average test score for a statistics exam will be u = 70, with a variance of o2 = 12. In a random sample of 8 students, the test scores are 65, 73, 74, 68, 70, 74, 69, 71, giving us the sample statistics i = 70.5 and s? = 10. Assume a normal distribution of scores. Answer the following questions to determine if...
Show that the mean of a random sample of size n is a minimum variance unbiased estimator of the parameter (lambda) of a Poisson population.
Please answer all parts, and show complete work. 6. (a) A finite population with N = 450 has a mean u = 112.5 and standard deviation o = 17.3. For samples of size n = 41, answer the following. The variance is for the sampling distribution of the sample mean X. (b) Random samples of sizes n1 = 32 and n2 = 40 are to be drawn from two independent populations. = 12.3 M1 01 = 2.9 M2 = 9.8...
Please give explanation................................................. Multiple Choice. Select the best response 1. An estimator is said to be consistent if a. the difference between the estimator and the population parameter grows smaller as the sample b. C. d. size grows larger it is an unbiased estimator the variance of the estimator is zero. the difference between the estimator and the population parameter stays the same as the sample size grows larger 2. An unbiased estimator of a population parameter is defined as...