Prove that the sample variance is an unbiased estimator for the population variance. That is, show that

Q: how to calculate the variance?

A: Given  The data is as follows: Overall mean = 4.07 Variance = 0.00130 SD = 0.1140

Q: The assumption of homogeneity of variances was tested by Levene’s Test, F(2, 432) = 4.61, p < .001.…

A: The hypothesis is, Null hypothesis: H0: The variances of groups are equal. Alternative hypothesis:…

Q: The Analysis of Variance (ANOVA) is used to determine if there is a difference between a selected…

A: ANOVA, the analysis of variance is the technique used to check if there is significant difference…

Q: If the null hypothesis is true, this means that there is no real difference between sample means and…

A: If the null hypothesis is true, this means that there is no real difference between sample means and…

Q: The homogeneity of variance assumption stipulates that, O the two samples have equal variances O…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Example 2: Calculate the standard deviation and variance for each set of sample data. Make sure to…

A: Let X denotes the scores of students from face to face class &amp; Y denotes the scores of students…

Q: If we delete the largest observation from a sample, then the sample mean and variance will both be…

A: The mean is the average of a group of numbers, and the variance measures the average degree to which…

Q: What is sample variance?

A: In very simple words, Sample variance means the variability in the sample around its average value.…

Q: True or False In general, a sample with a large variance is more likely to produce a significant…

A: Note that as the variance increases, p-value also tends to increase. To produce a significant…

Q: How do you find the standard error estimate of two disjoint populations, assuming they have the same…

A:

Q: A quality-control manager was concerned about variability in the amount of an active ingredient in…

A: Given data: Sample size = 21 To find: What is the probability that the sample variance of the amount…

Q: Which of the following is not desired property of the point estimator? A. maximum likelihood B.…

A: Point estimators are functions that are used to estimate a population parameter's estimated value…

Q: It is defined as the maximum likely difference between the observed sample mean and the true value…

A: Here  Sampling Error is defined as the maximum difference between observed sample mean and…

Q: The "true" variance is also the population variance True False

A: # Relation between True varience and population varience ?

Q: When is the population standard greater than the population variance?

A: Variance: The variation between each observation from its mean is known as variance. The greater the…

Q: i) What is the moment generating function of the sample mean? ii) What will be the mean of the…

A: It is given that Xi , i = 1, 2,. .......,10 follows given pdf f(x) i.e N(0,1)

Q: Let X and Y and Z are uncorrelated random variables with the same variance. Find the correlation…

A:

Q: Why is the unbiased estimator of variance used?

A: the unbiased estimator of the population variance, corrects the tendency of the sample variance to…

Q: To conduct a hypothesis test comparing two population variances, both pop must be normally…

A: Assumptions for two sample variance test: Two populations should be normally distributed. Two…

Q: What is the quare root of variance?

A: Given : Variance (σ2) is given

Q: If other factors are held constant, the larger the value of the sample variance, the lesser the…

A: The formula for a t-statistic or z-statics is : Z , t = X-Meanstandard deviation If we have a larger…

Q: which one is more precise sample variance or population variance

A: We want to tell you which one is more precise.

Q: If other factors are held constant, as the sample variance increases, the estimated standard error…

A: Given: Sample variance increase and effect on the estimated standard error

Q: in statistical inference, a sample ............ is referred to as the point estimator of the…

A: Point estimate : A point estimate of a population parameter is a single value of a statistic. For…

Q: The formula for total variance (SST) is

A: Solution:-

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: What is formula for the variance of the population?

A:

Q: It is known that the population variance equals 522. What is the sample size that needs to be taken…

A: It is given that:

Q: TRUE OR FALSE. If the population variances are unknown but can be assumed to be equal, a pooled…

A: Given the statement  that if the population variances are unknown  but can be assumed to be equal, a…

Q: what test is used to determine whether two population means are different when the variance are…

A: Solution :  when the variance are known and sample size is large then we use z test to determine…

Q: What is the best point estimate for the population's variance if the sample variance is 41?

A: Given,sample variance(s2)=41

Q: If the variability between the different sample means taken from the same population is small, we…

A: If the variability between the different sample means taken from the same population is small, we…

Q: What is the symbol for the sample linear coefficient correlation?

A: Linear correlation coefficient is denoted by r.

Q: Show that E[Sample Variance] = Population Variance

A: Let s2 denotes the Sample Variance and σ2 denotes the Population Variance Let X1 , X2.....Xn are…

Q: Prove an efficient estimator for the average of a normal population

A: X~ Normal with mean= mu and variance= sigma^2 Find efficient estimator for the mean

Q: Illustrate the sample covariance of a sample with itself?

A: Sample Covariance is defined as  Let x and y be two variables. The sample covariance is defined as…

Q: Test the claim that the samples come from populations with the same mean. A ssume that the…

A: As given,  It is assumed that the populations are normally distributed with the same variance.  The…

Q: Analysis of variance is a technique used to conduct a hypothesis test to compare three or more…

A: Solution-: Analysis of variance is a technique used to conduct a hypothesis test to compare three or…

Q: persons required to recover Assume the population variances are not equal

A: Given: A recent study of 20 individuals.  That is sample size n1=20 the average number of therapy…

Q: If other factors are held constant, increasing the sample variances will have very little influence…

A: Effect size : The size of the effect indicates how significant the association between variables or…

Q: The number of degrees of freedom for the two-sample t-test are the same regardless of whether or not…

A: The degrees of freedom of two sample t test different when ‘population variance are equal’ and…

Q: It is not essential to know the value of the population variances to test for the equality of two…

A: Solution To test the equality of means the F test is used .

Q: a population with a known mean but an unknown variance.

A: We have to study a single sample's mean is being compared to the population with a known mean but…

Q: In analysis of variance, the F-ratio is a ratio of

A: F ratio is a ratio of 2 variances or two mean squares. Mean squares are simple variances that…

Q: Explain the circumstances under which we would need to pool the variance for an independent samples…

A: The pooled sample variance offers a higher precision estimate of the variance than the individual…

Q: A process that exhibits random variability would be judged to be out of control Select one: O a.…

A: Note- Since both are different questions, so according to our policy we can answer only one…

Q: Which outcome is expected if the null hypothesis is true for an analysis of variance? a. SSbetween…

A:

Q: Traditional statistics (means, variances, and hypothesis tests) are not used to evaluate the results…

A: The traditional statistics are used to evaluate the result means we use the critical values to make…

Q: The area of inferential statistics called hypothesis testing is a decision-making process for…

A: Introduction: Inferential statistics is the branch of statistics, that is involved in making…

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.