Question

4.

Setup:

Suppose you have observations X1,X2,X3,X4,X5 which are i.i.d. draws from a Gaussian distribution with unknown mean μ and unknown variance σ2.

Given Facts:

You are given the following:

15∑i=15Xi=0.90,15∑i=15X2i=1.31

Bookmark this page Setup: Suppose you have observations X1, X2, X3, X4, X5 which are i.i.d. draws from a Gaussian distribution with unknown mean u and unknown variance o? Given Facts: You are given the following: x=030, =1:1 Choose a test 1 point possible (graded, results hidden) To test the null hypothesis Ho: p= 0 versus the alternative hypothesis Hí: 4 + 0 using the data above, which of the following test(s) is appropriate? (Choose all that apply.) t-test N Z-test: i.e. the test based on the central limit theorem Wald's test Submit You have used 0 of 3 attempts Save

Answer 1

t-test is appropriate for testing given hypothesis using given data 12- test is used for large sample size Here, nis 5 which is small & Wald test is used for asymptotic normal data. To find unbiased sample variance: UN ) - N-

n-) . (5x 1.31) - (.90)? 5-1 3= 0.8275, s = 0.83 one o upto two decimal 3) ME: û - x = 0.90 72 = S2 = 0.83 4) - T test: To test, Ho: M = 0 under Ho test statistic uto. Vs H is, tnt ta X-Mo o Sun 0.goo 10.83/5 t = 2.2089 t-statistic = 2.21 led=0005 5% of samples to wrongly reject Ho Critical value: tai, /2 = t4, 0.025 = 2.176

I Here, t-statistics (2.21) C tn 1,91212 • 776) .. Accept to or fail to reject Ho. 5) Confidence interval: grlo 10.90 – 2.71640.9110 0-90+ 0.9110 .0-90 + 2-176x 0.91 2 10.90-1.13097, o.g0+ 1.13097) (-0.23099, 2.0309) lower bound a = -0.23. Upper bound B = 2.03.