Question

n Sample 1 10 17.4 Sample 2 10 19.1 X Assume that both populations are normally distributed a) Test whether H17 * H2 at the a = 0.10 level of significance for the given sample data. b) Construct a 90% confidence interval about H1-H2 S 3.9 4

Answer 1

a) Hypothesis test: He: M = M₂ NHii M, & M₂ Test & falfistici Here would like to to perborm 4- test. The test statistice testat X - X tnth nith, -2 So 1 2 1 + + 2) where pooled s. 11 Sp Sp = (11-1) s + 12 ) sa nit n₂ - 2 tstat 1704 1 gol -0.244, (10:1) 33.9+(10-134 64 +7) 10 10-2 the Pr value 2 (t> tarat) bar det 20120-2 =18. P-value Oi 8103. ib p-valuca Decision Rule; can reject the Ho we this Here Result: p-value =0.8103 > 2=0.10 result is not statistically significant. we can't reject the Ho.

(b) we Here we construct go% confidence interval for Hi Me consider to vacate with pooled pooled s. is considered pirotal quantity such that •{ t = (x - x) - (14, N.) ag t.no ne the 2 so G I + 1) no predefined 3p = pooked so introduce two and Constanta tal t4/2, 0-1 we n-1 such that Ф tala, no n-1 PL sta tele, n-1 J = 18. 3) P[- tape, ny s (x-7) - (H, H2) 1th testo + £) < (x,- tz) - (4 Hz) s talent Se is الا th he [- talan- N-1 no - (4,74₂) E (IR) I take, ny se no I (104) 3.95 +(10-1) 4 - 3.95. Sp hay 10+1o-2 l-a-oiro 2/2 20.05 toos, 18 = 1.734 (M - M2). E (17.4-19.1) 7 1.734 3.95 3-95/6+ ++)] {17.4-191) 7 1.73481-467) = (-4763, 1.363)
if you have any doubt you can ask me. And check the calculations