To show that an estimator can be consistent withoutbeing unbiased or even asymptotically unbiased, considerthe following estimation procedure: To estimate the meanof a population with the finite variance σ2, we first takea random sample of size n. Then we randomly draw oneof n slips of paper numbered from 1 through n, and if thenumber we draw is 2, 3, ..., or n, we use as our estimator the mean of the random sample; otherwise, we use theestimate n2. Show that this estimation procedure is(a) consistent;(b) neither unbiased nor asymptotically unbiased.

Q: Although you can computea z-score for a single score (a sample of n - 1), it is impossible to…

A: we need to explain the statement that we can compute a z-score for a single score (a sample of n-1),…

Q: A U.S. government survey in 2007 said that the proportion of young Americans that earn a high school…

A: Solution: Given information: n=100 Sample size p= 0.87 Population proportion.

Q: Suppose that we have disjoint normal populations A and B with unknown population variances.…

A: Given, Suppose we have a sample of size 10 from population A and a sample of size 15 from population…

Q: If the range of X is the set {0,1,2,3,4} and given that each outcomes are equally like to occur,…

A:

Q: From a Poission distribution with mean 1, let y1, y2, Y3, ... , yn be a random sample. The following…

A:

Q: When data are collected in a statistical study for only a portion or subset of all elements of…

A: A sample is a part of the population, which is selected from the population and if the sample is…

Q: Consider the following population: (6, 7, 8, 9). For this population the mean is U=6+7+8+9 4 Suppose…

A: Population : {6,7,8,9}  Sample size =2  Without replacement :  6,7 6,8 6,9 7,6 7,8 7,9…

Q: The Null Hypotheses is: H0: μ1 - μ2 = 0 Based on these hypotheses, find the following. Round…

A: The test statistic and P-value value is obtained by using EXCEL. The software procedure is given…

Q: to population variance, we get an estimate of the sample variance by ① . This is known as ② . This…

A: Population Mean and Variance μ = 1n∑i=1nxiσ2 =1n∑i=1nxi-μ2 Sample mean and variance x¯=1N∑i=1Nxi…

Q: To compare the mean lengths of time to recovery after two surgical procedures I and II, 10 patients…

A: To check whether there is any difference in the mean recovery time after surgical procedure I and…

Q: Suppose that you draw a random sample from a population where you know the population mean is 36 and…

A:

Q: Assume two populations, one of size 15 and variance 12 and the other one of size 10 and variance…

A: Given, n1=15, n2=10, σ12=12, σ22=7.6 The combined standard deviation is given by,…

Q: Consider that X1, X2 X3, X4, X5 is an independent random sample where X, follows a normal…

A: Solution: Given information: Xi~N(μx=3.2, σx2=3.2)      i= 1,2,..,5n1=5  Sample size of XYi~N(μy=…

Q: Suppose you know that the population variance for the weight of tractors is 4,000,000. What sample…

A:

Q: Suppose you are constructing a Cl for a mean using the T-distribution and your sample size is 17.…

A: Degrees of freedom = n-1

Q: In a 25-Question multiple-choice, there are five possible answers of which one is correct. Let X:…

A: X=number of correct answers  n=number of trials=25 p=probability of success= 1/5 =0.2 [because each…

Q: Suppose Y is distributed with mean=80 and variance=100. You obtain a large number of samples each of…

A:

Q: Suppose that we have disjoint normal populations A and B and we want to find the standard error…

A: Denote μ1, μ2 as the true averages of populations A and B, respectively.

Q: Suppose that we draw a sample of size 49 from a population which has an incomplete gamma…

A: From the given information, Consider, X is the random variable that has incomplete gamma…

Q: If 446 rods are sampled at random from the batch, what is the probability that the mean length of…

A: Here we have given information, A batch of steel rods produced at a steel plant have a mean length…

Q: i need Solution with using 50 values of data Data: 25 2 7 1 21 7 21 27 27 8 21 28 4 26 23 10 17 20…

A: data :…

Q: Assume that the population consists of only these eleven data points for y and z. Construct one…

A: It was stated to assume that the population consists of only these eleven data points for y and…

Q: A teacher is interested in assessing whether or not there is the same amount of variance in the…

A: Given, A sample of 15 boys had variance 460 A sample of 13 girls had variance 1400

Q: Body Mass Index is a measure of body shape. Duran et al. (2013) investigated BMI in Texas youth. In…

A: Solution:  The 95% confidence interval for difference in means μ1-μ2 is  ( -2.9517451, 0.2764086)

Q: Before using these variance estimates, what must we calculate?

A: Before using any variance estimate we should check whether it is biased or unbiased and calculate…

Q: The proportion of all adult shoppers who make a written list of the items they need before going to…

A:

Q: transect is an archaeological study area that is  mile wide and 1 mile long. A site in a transect is…

A: Given : Let x represent the number of sites per transect. In a section of Chaco Canyon, a large…

Q: You observe a sample of five numbers between 0 and 10. Their median is 5 and their mean is 5. What…

A: The numbers are between 0 to 10. The mean is the ratio of the sum of all observations to the total…

Q: A large airline company called Fusion Fly monitors customer satisfaction by asking customers to rate…

A: The mean is 4.10 and the standard deviation is 1.33.

Q: A new chemical process is run 10 times each morning for five consecutive mornings. A plot of yields…

A:

Q: Define the bias of an arbitrary estimator and show that if an estimator is unbiased then the square…

A: Let, T be an arbitrary estimator of parameter θ with expectation E(X), variance V(X) and Mean Square…

Q: A simple random sample of 100 water meters within a community is monitored to estimate the average…

A: Introduction: It is required to estimate the true mean of daily water consumption.

Q: One sample has SS = 60 and a second sample has %3D SS = 48. %3D a. If n = 7 for both samples, find…

A: SS for one sample =60 SS for second sample =48

Q: An average of many different studies of handedness indicate that in a random sample of…

A: Percentage of men left-handedPercentage of women left-handedTotal menTotal women

Q: 9. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson…

A:

Q: A researcher takes sample temperatures in Fahrenheit of 18 days from Pittsburgh and 16 days from…

A: Given that, a researcher takes sample temperatures in Fahrenheit of 18 days from Pittsburgh and 16…

Q: Suppose you needed to test the claim that the two samples described below come from populations with…

A: We have to find the degree of freedom and test statistics.

Q: One sample has n=7 and SS=35 and a second sample has n =17 and SS =45. What is the pooled variance…

A: Given information: The two sample statistics is given as, Sample 1 n1=7SS1 = 35 Sample 2 n2 = 17SS2…

Q: Select one: OA ± 1.645 OB. ±1.96 OC. 3.841 OD. 2.706

A: Let  be the population proportions of workers who would like to attend a self-improvement course in…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.