Question

114 Find the t critical values suggested by the given data. a. H u 12; H: u 12; n = 27, a = .05 b.Hiu500; H: u > 500; n = 17, a = .10 c.Hai un 10.75; H; u < 10.75; n = 29, a .01 d. Hoi u 75 H:u # 75; n = 24, a = .05 e. Hoiu 98.4; H: u < 98.4; n 12, a = .05

Answer 1

We know that the Critical value: t critical value is used in significance testing It is the value that a test statistic most Exceed in order for the holl hypothesis to be rejected Now the to critical value is the cut off between retaining or rejecting the null hypothesis * whenever the t- statistic ů farther from o than the t - Critical value, the null hypothesis is rejected , otherwise, the noll hypothesis is retained Given that Ho: M=12 Hi : M & 12 and n=97 , 4-0.05 where df = noi - 27-1 de = 26 Two talted & It allows us to are different from one another determine if two means

ît å as our a Calpha value) is 0.05 the test op two-tailed h * c(a/9, -1) +(0.05, 27-2) tCo-oas, a6) = 2.056 b) to : H 1500 ; # :M7500 where n=17 and 2 = 0.10 If the null Expresses less or equal, the alternative Expresses greater than of the holl Expresses greater (ory Equal, then the alternative than less Express & The Alternative hypothesis has the less than operator it will be legt tailed test If the alternative hypothesis has not Equal to operator it ý tuo tailed (left and right) test It ů Right tailed test de=n-1 = 17- = 16

tla.n-1) +(0.io, 171) +10.10, 16) from the table) 1.337 C) Hot > 10.ts; H H1075, h: 29 2:0.01 . de anal = 99-1 It ý left tailed test art (a.n-1) t(0.01, 29-1) = -t(0.01,22) = -2.467 4 2 = 0.05 d) Ho f= 75 H,:4&75, n=24 tailed test It ý two a -005 h=24 = 24-1

tala, 24-1) to, 23) t(0.025, 23) = 2.069 e) Ho M >984 ; t, :ME 98.4 &n=12, 2= 0.05 . It uw left tauled test et carna) = -t(0.05, 12-1) = -t(0.05,11) =-1796 z