MidtermI_2008_PracticeExamIsol-1

# MidtermI_2008_PracticeExamIsol-1 - MidtermI_PracticeExamI...

This preview shows pages 1–3. Sign up to view the full content.

MidtermI_PracticeExamI Solutions 1. The appropriate hypotheses are REG IMP a REG IMP H H : : 0 (1st – Assuming equal variances): The test statistic will come from a t-distribution with 123 degrees of freedom. Approximating this distribution using a 120 t distribution, our decision rule is Reject 0 H if 98 . 1 120 , 025 . 0 t t , and do not reject otherwise The pooled estimate of standard deviation for the two populations is 1536 . 8 4815 . 66 2 75 50 ) 232 . 9 )( 74 ( ) 178 . 6 )( 49 ( 2 2 p s The test statistic is then 3714 . 2 4886 . 1 53 . 3 75 1 50 1 ) 1536 . 8 ( 99 . 31 46 . 28 t This value exceeds the critical value from the decision rule. Hence, we reject 0 H and conclude that the “improved” design does appear to change the level of hydrocarbon vapors emitted. (2nd – Assuming unequal variances): The test statistic assuming unequal variances is then 5611 . 2 3783 . 1 53 . 3 75 ) 232 . 9 ( 50 ) 178 . 6 ( 99 . 31 46 . 28 2 2 t We will use a t-test with DF=100. the t -table does not contain an entry for DF = 100, so we can approximate using either 60 t or 120 t (in this case, we play it conservatively and use 60 t ). Our decision rule is thus Reject 0 H if 2 60 , 025 . 0 t t , and do not reject otherwise. Our conclusion is the same as with the equal variance assumption: we reject 0 H ; hence, there is significant evidence to suggest that the “improved” design changes the level of hydrocarbon vapors emitted.

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

View Full Document
2 (a) Summary of Fit (for the Regular device) RSquare _0.776_ Root Mean Square Error 4.40 Mean of Response 31.99 Observations 75 Analysis of Variance
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

MidtermI_2008_PracticeExamIsol-1 - MidtermI_PracticeExamI...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online