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# Sp09_EC41_key - EC 41 UCLA — Sample Problems#9 RE Ch 7...

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Unformatted text preview: EC 41 UCLA — Sample Problems #9; RE Ch 7 and 10 W I) {an F A pooled two sample t—test assumes the true standard deviations of the two populations are the same. ii) T or®Suppose X is not distributed normally The sampling distribution of X from simple r om samples will approa a normal distribution as the number of samples increases. W09” (M in»? I n when OESFK’V/HT-VM ﬁl iii) T org )lhe Null Hypothesis ofa matched pairs‘Ft‘eEf'isthat the difference (e.g., between a pre and post test) for all obse 'onal units (e.g., teachers) is zero, Ho: xi =0. ivﬁr F The Null Hypothesis of a two sample t-test assuming unequal variances is usually that the true mean difference between two different populations 1 and 2 is zero, Ho: u} - p2=0; which is equivalent to Ho: pl = u; v r F If I? is further from the value in the null hypothesis, then the p-value will be smaller, all else constant. vi r F The p-value for a two sample t-test with unequal variances given by Excel is typically smaller than that which we calculate by hand. This may reﬂect the higher degrees of freedom used in Excel’s calculations. 2) A group of people are given tests before and after training. Scores on the pre—test of 4 people randomly selected people are X. = 30, 30, 40, and 40. Scores on post-tests (aﬁer training) for 3 randomly select -_ or e to are: X2 = 50, 60, and 70. Assume test scores are normally distributed, but standard deviations may differ. U - 2 for the degrees 0 eedom. 33 —[ = 2, a) Form a 95% conﬁdence interval for the difference in population means, it: ~ to ?1_;Ii 751i 5' 5‘ ,> 50—52? I 14.31)") tar. +3” TIT l W; a» 4 m ‘l Q52) (11‘ 251+ ”3036945583 Calm/lath»? £959. {:75 £1: 3.7735 32333 f 27.7? gums t'- . r [54 \$560 s,= m SEW; (.2 1952.79) 64.45249 x) 1)) Perform a Mo sample t—test of the null hypothesis that the scores on averag improve sus an alternative of no change (equal means). Show your calculated t—test statistic. Are results si ' can at the 5% level? Hi i I“ 1 34/7. [9 se the smaller of(n.—l) or (mg—l) as the degrees of freedom). 90 5W. 3'1ch #4 by; OH Do NOT assume the true stande deviation of gorges before is the same as that of the scores after. 2 2 59:23 13.12: i 6:ch p _: EYES 5‘6”!th FtMlL‘l/lﬂlﬂl ‘Y—Lgl'ab‘? = i 3873 S49; 1420 .DS— ng.01§ @811!)th “5F ”'50? from {niacin/ﬁr ; 0 \$— . 3) Recall the data from #9, Sample problems 8: \____—/3’__l_2_32__ Store 1 2 3 4 5 6 7 8 9 10 f“ r 550 Before .10 11 19 12 7 8 5 20 20 14 'ZE‘X’B \$3 ‘ After 15 17 13 11 9 15 4 25 26 1919.1)‘24 \$4 ., 5.7a a) Find the 95% Conﬁdencc Interval for the mean difference (After - Before) in sales, Assume the 10 stores “after” need not be the same as “before “ so you do NOT use matched pairs procedure. Deﬁne difference as after minus before, so the mean difference is positive. interval? i £1 b) The connection between sales and individual store was lost/So now we have l0 before observations and 10 aﬂer observations from two distributions that are approximately normal. Use a two sample Host to ﬁnd a tcmugmd and range for the p-value when Ho: sales remained the s ' es increased. As in part “a”, domulation Stan ar evr ations are t 6 same before and after (so you will not compute a “pooled" estimate of standard deviation). bum: {911-91, - Q : 0H1: one Jailed E32 t-Mﬁ‘ W #3404)? ll) )0 ANOVA d)_‘ SS MS F Four Observations Regression 1 1122.002 1122.002 10.01707 U.S. com Ln'eld Residual 2 224.018 112.009 Year (X) Yield (Y) Total 3 1346.02 1965 74.1 _ l 975 86.4 Standard 1985 118 Coeﬁicients Error {Star P-value 1995 1 13.5 Intercept -2368.04 937.1596 —3.06035 0.092237 Year 1,498 0.473305 3.164976 0.086999 Regression Statistics R Square 0.83357r Standard Error 10.53343 4) Consider the results above for the regression cj‘k Yield of com (Y) on Year (X). a) Write the estimated regression equation. x; — 2 5 6 a +0. 5) )6 GP \/ = ~226910-91x 7‘6") b) Interpret the slope coefﬁcient. What is the relationship between year and yield? date; if) ; (1C: “4.235 ; 3/;le mam/2g, #1 /. 5” each/1411‘. A Ymr 21.; 0) Calculate the sample standard deviations fOr x and y: 5x = i 2 0i 5y: d) What Is the sample correlation coefﬁcient r? (square root R2 is it ositive? can verify with equation on pg.1 14) i 9356‘”? 2,913 2p I'll/“6‘5 i“?— lerg'zcﬂizgj / e) Use the technique on page 591 to calculated a t test statistic 19m for the sample correlation 75. l 6 How does this compare to the t-test statistic on the slope coefﬁcient on the X variable, Year? 0 EH3 We ; LLCHh- W 3/5 t) Interpret this ~ do you reject or accept the null hypothesis that the true correlatiore p= 02]: 0010030 OZ: Ai'v?‘ BEIEH‘ H3" P20 1210190,; ”025 LOW—112:; ”Lewis aliﬂ‘tiaD/My 110 1145/3743 'F 2_q; [-1.303 4023 < 9.193%; < .03- ‘0’; (P1511611 (-10 3,) What 15 the PTGIgCtidm) cro 'Id 111 005" (’a‘l’i l'f’li pm A = 1295 2.909 141 019m magma ML / :2 0M 0 AL “Hist 45 _ 5315620119) P ~ —;~,09’M44 .097 Mill/Lelia: 6/0/69 hag. harm/MM! om \/ ...
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