{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

L8 Comparing Population Means and Variances

# L8 Comparing Population Means and Variances - Comparing...

This preview shows pages 1–2. Sign up to view the full content.

Comparing Population Means and Variances. Testing for the difference between means in two populations. Given two independent random samples X 1i , i = 1,. .,N 1 and X 2j , j=1,. .,N 2 (the independence is both between and within the samples) from two populations which are respectively N(! 1 ," 1 2 ) and N(! 2 ," 2 2 ) the sample means, which will be independent of each other, will be distributed: 22 12 11 2 2 , ,; XN NN ±± ²² ³´ ³ µ ¶· ¸¹ ¸ ´ · ¹ (Note that if the distributions are not normal the sample means will still be approximately normal by the Central Limit Theorem). Since it is a property of the normal distribution that sums and differences of normal random variables are also normal with a variance equal to the sum of the variances in both cases (we shall demonstrate this in a later chapter) it follows that: 1 2 , XX N µº º » ± which, when the variances are known, can be used to test hypotheses about ! 1 - ! 2 in a fashion similar to the tests for a single population mean which were outlined in course notes 5. This follows since transforming to a Z variable we have: ¼½ 1 2 (0,1) ZN µº º º ¾ » ± which for hypothesized values of !

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

L8 Comparing Population Means and Variances - Comparing...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online