Question

4. You are given the following information on a random sample from a normal loss distri- bution with mean : • The sample mean is 42000. • The sample standard deviation is 8000. • There are 25 loss observations in the sample. Let to be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta for specific combinations of a and v: v = 23 v = 24 a = 0.05 1.714 1.711 a = 0.025 2.069 2.064 a = 0.01 2.5 2.492 + 45000 at which value of a would you To test hypotheses H:= 45000 versus HQ: reject the null hypothesis? • Reject H, at a = 0.01 • Reject H, at a = 0.02, but not at a = 0.01 • Reject H. at a = 0.05, but not at a = 0.02 • Reject H at a = 0.10, but not at a = 0.05 • Do not reject H. at a = 0.10

Answer 1

solution: The provided Information to the quatre you are given the tollowing Informatly on a Eandom sample from a normal loss distributres with mean el touc the sample mean B 4.2006=7 the sample standaed deviathan s= 8000 There arenes loss observatten in the sample te naas 8-62000 s-8000 To test Ho Ho hypothesis - 48000 Versus M445000 - Now, to tind - Stoctistic, le tcal = {-calewated value to ona 141 4 - 142000 -4-5000 - 3000 200. 0% 800b/s _JAL 3000 1.87 _IL 1600 It) - tealcatated = 1:8751 From table 0 20.0123 Izzal a 2.5 Here tcal (t23,0.01 Hence Accept Ho Rerect Ho at a-o.ol is not true statement Similarly for =24 2 -0.02 =23 t23.0.02 = 2.17 toom table 1 Here teal tesou2 Hence neeept to Similarly for v=24 Hence pegect Ho at a=002 but botanool tement is talse

3) 2005 -23 toos, 23 = 1.714 (from tables Here Hence tcals toos, 23 200 to old targe t oo5 Repeat Ho at x 20.05 toor 24 =1.71 200tc from table) not Heal tral toor, 24 tt Hence Rercet to at a 2005 oo but rool ra23 ok v= 24 to.og, 23 - 2.760 (from table) & flere tral (toos, 235 Hence Accept Hoe to all toon but hot at & 20.62 Hence This Reject to statement at a 20.05 B true 4) 2201 V=23 -to. 1123 = 1.31946 Here teal to.),23 lbhom table) on a 22108 21 Hence Reject to at &20.1 ozung beg similarly, anal, vazo tangos to1124 = 1.317836 (brom table) Here tral 7 toyi29 Hence Refect Ho atato 1 20.05 toos V=23 1.719

Here tcal toor, 23 Reject to at 0.05 200 + bet Reject to at a=0.) but not this steedement is false at a 20.05 = 23. 5) oot azo. 10 to 1,23 = 1.31946 Here adot cards teal to.1,23 & Hence Reject Ho at o.lt Similarly Lol N=2& Otud 2002 I tral toiley ust z loanoto Hene pgect Ho at arolo Ho at do I this statement Do not pereat B false conclusion 1. o e to of Repeat Ho at doos but not at 20:02