10 lid 3. Consider a test that measures the sample variance L'atºy? of an electrical signal to assess interference. Supp

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10 Lid 3 Consider A Test That Measures The Sample Variance L Atoy Of An Electrical Signal To Assess Interference Supp 1 (259.44 KiB) Viewed 31 times

10 lid 3. Consider a test that measures the sample variance L'atºy? of an electrical signal to assess interference. Suppose that Y, N(0,1) if there is no interference and Y: N(0, 2) if there is interference ie, the variance is doubled. For this question you may find the Xío table below useful. The top row provides the CDF and the bottom row the quantiles. 0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 2.56 3.94 4.87 6.18 7.27 8.30 9.34 10.47 11.78 13.44 15.99 18.31. 23.21 iid w 1 id (a) If the null hypothesis is that there is no interference, write down Ho and HA in terms of possible values of a where Y, " N(0,1). [4] (b) Design a level a = 0.05 test to decide between Ho and Ha, using the pivot approach. i.e. find k such that you reject Ho when Ỹ > K. Hint: Start by calculating a = PlÝ > k\Ho) and use the fact that [~ xã when N(0,0%). 1 [7] (c) Find the probability B of concluding the interference is absent when it is in fact present. [5] (d) If you observe ğ = 2, is there enough evidence to reject Ho at significance level a = 0.012 (e) If you would like the probability of missing interfence when it is present to be less than 10%, what is the smallest significance level that we can achieve? Comment on your finding. Hint: evaluate the critical value k corresponding to this value of B. [7]