Let Y 1 Y 2 , , Y n1 , be a random sample of n 1 observations from a normal distribution with mean 1 and variance 1 2 Let X 1 , X 2 , , X n2 be a random sample of n 2 observations from a normal distribution with mean 2 and variance 2 2 Assuming the samples were independently selected, show that has an F distribution with v 1 (n 1 1) numerator degrees of freedom and v 2 (n 2 1) denominator degrees of freedom F

Question: Let Y 1 Y 2 , . . . , Y n1 , be a random sample of n 1 observations from a normal distribution

Let Y₁ Y₂, . . . , Y_n1, be a random sample of n₁ observations from a normal distribution with mean μ₁ and variance σ₁². Let X₁, X₂, . . . , X_n2 be a random sample of n₂ observations from a normal distribution with mean μ₂ and variance σ₂². Assuming the samples were independently selected, show that has an F distribution with v₁ = (n₁ - 1) numerator degrees of freedom and v₂ = (n₂ - 1) denominator degrees of freedom.

F =

Step by Step Solution

★★★★★

3.45 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We want to show that the statistic F F S12S22 2212 has an F distribution with v1 n1 1 numerator degr... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics For Engineering And The Sciences Questions!

Let X1 and X2 be a random sample of size n = 2 from the exponential distribution with pdf f(x) = 2e2x, 0

Let X1 and X2 be a random sample of size n = 2 from a distribution with pdf f(x) = 6x(1 x), 0

A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population): x1: New England crime rate Another random sample of n2 = 12 regions in the Rocky...

Q6. Suppose that X =61 + 52, where 1 N N(6,1), 52 ~ N()\\6', A2), and 1 and 52 are in- dependent. Here, A 2 1 is a given constant, and 6 is a unknown parameter. (iv) Let X 1, X 2, - - - ,Xn be an...

Hi, it's me again Thanks for helping me with the answer last time d u 1. (a) Let Y1, Y2, ..., Yn be a random sample from a Bernoulli (p) distribution (i.e. Binomial(1, p)). Show ELI K is a minimal...

\f 1 Let X 1 , X 2 ,....., X n is a random sample from a normal distribution with mean and variance 02 known. Then probabilily density function 1 x i 2 0 1 f xi 2 e , xi , 0, 0 2 By def, Likelihood...

STA5326 - Mathematical Statistics - II Homework # 3 1. If X 1 , X 2 ,..., X n is a random sample of size n from N ( , 2 ), , show that n n n 2 2 X j , X j or X , X j = = j 1 j 1 =j 1 is a sufficient...

11/26/2016 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. My sites / 16F-STATS100A-1 / HOMEWORK / Fall 2016- Homework 12-Due Thursday 12/1, before 8 PM. Must submit...

1 If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.5 minutes and a standard deviation of...

v12 The Kruskal-Wallis Test Suppose that we have independent random samples of n, ny, ... lx observa- tions from K populations. Let n = 1 + 12 + ... + 1k denote the total number of sample...

What is the purpose of a cost of production report?

A survey of U. S. chief financial officers provided compelling evidence that managers are willing to take extraordinary measures to achieve financial earnings targets. For example, the survey found...

Your friend Larry is deciding whether to break up with his current girlfriend, Lucy. He tells you that his number-one reason for staying with her is his tattoo, which says I love Lucy. Based on...

Full and free communication, regardless of rank and power.

When the out-of-control ARL corresponds to a shift of 1 standard deviation in the process mean, what are the characteristics of the CUSUM procedure that has ARLs of 250 and 4.8, respectively, for the...

Consider the single-sample plan with c = 2 and n 5 50, as discussed in Example 16.11, but now suppose that the lot size is N = 500. Calculate P(A), the probability of accepting the lot, for p = .01,...

A sample of 50 items is to be selected from a batch consisting of 5000 items. The batch will be accepted if the sample contains at most one defective item. Calculate the probability of lot acceptance...

Monk Consortium Corp. ( Monk - Con ) had sales of $ 1 , 7 2 0 , 0 0 0 last year on fixed assets of $ 3 9 5 , 0 0 0 . Given that Monk - Con's fixed assets were being used at only 9 6 % of capacity,...

Master it! Chapter 7 Chapter 7 Chapter 7 - Master It! In practice, the use of the dividend discount model is refined from the method we presented in the textbook. Many analysts will estimate the...

a bond's price/coupon payment /par value a bond issuer is said liquidation/bankruptcy/default a bond contract sinking fundation provision/call provision/convertible provision a bond's call...