Question

Please be as clear as possible.

Textbook - Applied Statistics and Probability for Engineers by Montgomery, 6th Edition

PART 1. For each of the following statements, circle the letter “T” if it is true, and “F” if it is false. TF If events A and B are mutually exclusive, they must be independent. т F P[A B C] P[CB] P[B] = P[CAB] P[AB] P[B]. T F If the 95% confidence interval for a particular situation is (-5,5), then the 90% confidence interval would be narrower; that is, (-5 + x, 5 - x), where x > 0. TF For a continuous random variable X, if its PDF f(x) is constant, then X is uniformly distributed TF The CLT (Central Limit Theorem) states that the distribution of the sample mean X approaches the normal distribution with mean u and variance o2 if the Xi's (i = 1, 2, ..., M) are identically distributed with mean u and variance oʻ, as N becomes sufficiently large. T F Let û x, and Û2 x, be two estimators for the population mean. û, is a better estimator than ûj. PART 2. From the list below, place on the left of the formula the number of the correct label next to each symbol. Some labels may be used more than once, some others may not be used. 1. Population mean 2. Population variance 3. Population standard deviation 4. Sample mean 5. Sample variance 6. Sample standard deviation 7. 8. 9. 10. 11. 12. Variance of sample mean Standard deviation of sample mean Sample variance of sample mean Sample standard deviation of sample mean Error mean square None of the above E[X] (N-1)N E[(x - 21 N E[X4) -u? OX S #$&; – F) X E[( X - u)?] N

Answer 1

distributed with mean M. and variance as Answer: part ! mutually exclusive, they True T a) If events All are must be independent 6) True (1) PLATBOY ACIB) P[B] =PICIAMB] P[A16] P[B] 1) y The 95% confidence intenol for a particular situation is (-5,5) then the 90% confidence interval would be narrower Hout is Es+x, 5-x), where x>0 • True (T) d) For a continuous random variable Hits PDF F(X) is constant, Thon X is uniformly distributed True (T) c) The CLT states that the distribution oli sample mean x approaches the nominal distribution coith mean Mond variance g? if the xis (i=1,2, N) are as n becomes sufficiently large - True It) I Let M, 2 x and a 4x be two estimators for the population mean a better estimator than û, - False (5) identically

part 2 2 S 41 EX] {(x; - x)2 (N-DN 8 E[X-M] 9 E[x]-M 3 ox 10 6 2110 2 4 € (x; -7) ² E{CX-1)] х 1 M 4 7 sample variance Ir population mean 2- Population variance 3 - Population Standard Deviation 4 sample mean S sample standard deviation variance ay sample mieon standard deviation of sample mean Sample voriance of sample mean Sample standard deviation of sample means Enor mean square. None of the above 6 q 10 LI 12