# Let X = ( X 1 , X n ) be a random sample from N( 1 , 2 ) and let Y = ( Y 1 , Y m ) be a random…

- September 24, 2021 /
- ecommerce Development, web development, Software Development, Online marketing, Magento, Ecommerce

Let X = (*X*1*, **X**n*) be a random sample from N(1*, *2) and let Y =

(*Y*1*, **Y**m*) be a random sample from N(2*, *2). Suppose that we

wish

to test *H*0: 1 = 2 versus *H**a*: 1 _= 2.

(a) Show that the likelihood function *_*(X*,*Y) is a monotone

function of *T *2,

where *T *is the two-sample *t*-statistic that

uses the pooled estimator *S*2

*p *of the common variance 2.

(b) Let *S*2 1 be the sample variance for the *X**i *’s. Let *W *=(¯*Y *–*X *−* *0)*/**S*1,

where*_*0 is a constant. Find a constant *K *such that *KW*has the noncentral

*t*-distribution. Give the degrees of freedom and

noncentrality parameter _.