Question

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 for any shape of population distribution.

2.Select all true statements about sample variance, sample var(U), and SD.

(Recall: In the simulation, Variance refers to the sum of squared deviations divided by n and Var(U) S 2 refers to the sum of squared deviations divided by (n-1))

A) SD (Standard deviation) is an unbiased estimator of population standard deviation when population distribution is normal.

B) When sample size is small, Variance is a biased estimator but Var(U) is unbiased estimator of population variance.

C)The sampling distribution of Variance has a smaller standard error (varies less) than the sample distribution of Var(U).

D)When the population distribution is skewed, both Variance and Var(U) are biased estimator of population variance.

3. State whether each statement is true or false.

(i) We can construct a sampling distribution of other statistics such as sample range.

(ii) The shape of a sampling distribution is always the same as the shape of population distribution.

A) Both (i) and (ii) are false.

B) (i) is false, (ii) is true.

C) Both (i) and (ii) are true.

D) (i) is true, (ii) is false.

Answer 1

we know A sample mean is always unbiased estimator of Population mean. Ther fore statement in option A is False B) when distribution is symmetric both mean & sample median are unbiased estimator of population mean. Therfore statement in option B is True c) sampling distribution of sample mean is. INN(M. 6) sampling distribution of sample mee ma non(d, 767) we know, standard error for mear SE = vo for median, se = 702 = 5 S/n = 6 11.250 To S. E (median) > SE (mean) Standard esror of mean is less than S.E of median - statement in option c is True 1 sample mean is always unbiased estimator Population mean but sample median is not always unbiased - Statement in option is False Thus, A False B) True Trie False 8