Question

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Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether Hy Hy at the a=0.05 level of significance for the given sample data. (b) Construct a 99% confidence interval about 14 - My

Answer 1

bolyn. Given: Population 1 - 0=21, *, = 519 S, = 4,8 M₂ = 15 , X 2 = 40.8 S2 = 14.4 ay Aim: To test whether M, > 2 Ho: M, >l2 Cclaim) ; H, : 4, = 42 Null and Alternative hypothesis are A. Ho: M, >ll2 Hiil, = 42 Here Sample std dev. ove known so we use two sample t-test t = test statistics (X, Y) 51.9 - 40.8 5,292 (4.82 (14.402 21 15 + f nz 3.862789 ... •df = 2.8736 2.87 tes! Statistic for this hypothesis test is 2.81 For p-value using following Excel command df = n, +02-2 =R1+15-2=36-2=34 . P-value = *T T.DIST.RT (2.87,34) y test Slolistic . P-value = 0.0035 20.003 ..p-value boy hypothesis test is 0.003 Here a=0.05 bince pvalue <a: Reject Ho. Conclusion Box hypothesistesi Ans. C. Reject Ho. There is not sub?icieni evidence at 2-0-05 level 03 significance to conclude that elixMz by 99% confident = 2 = 0.01 =t 0.01, 34 = 2.576 :t=ta.no (two sided)

at the bor i estom mokropora poder confidence interal vor ll, ll2 is given by (3,-2) + E where E= morgen oz error .. E= tx 2 5,2 si + ni Az = 2.576 * (4.972 21 o399H (4.872 04.4.2 = 2:576* 3.862789 obor E= 9.9505 ... lower limit =H (71-72) - EI = (5):9-40-8) - E che 11.1-9.950s = 1:1495 1.150 Upper Limit ( X72) +E - 1:1 +9.9505 Dia tota 1867 4.9 Mb 21.0505 21.053 A 09-10 : The 99%. confidence interval obout Ujuz is the range from lower bound 0% 1.150 to an upper bound of 21.05)