- Please Answer All The Ff Questions 1 (95.18 KiB) Viewed 25 times
PLEASE ANSWER ALL THE FF QUESTIONS:
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PLEASE ANSWER ALL THE FF QUESTIONS:
PLEASE ANSWER ALL THE FF QUESTIONS:
= -= 3. Consider a test that measures the sample variance ✓ = 1410 Y} of an electrical signal to assess interference. Suppose that Yhd N(0, 1) if there is no interference and Y, id N(0, 2) if there is interference i.e. the variance is doubled. For this question you may find the xic 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 = = (a) If the null hypothesis is that there is no interference, write down Ho and HA in terms of possible values of where Y" N(0,2). [4] (b) Design a level a= 0.05 test to decide between Ho and HẠ, using the pivot approach. i.e. find k such that you reject Ho when Ý > K. Hint: Start by calculating a = PlÝ > K|Ho) and use the fact that I xã when y? yid N(0, 02). [7] (C) Find the probability B of concluding the interference is absent when it is in fact present. [5] (d) If you observe y = 2, is there enough evidence to reject Ho at significance level a = 0.01? [4] (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] =
= -= 3. Consider a test that measures the sample variance ✓ = 1410 Y} of an electrical signal to assess interference. Suppose that Yhd N(0, 1) if there is no interference and Y, id N(0, 2) if there is interference i.e. the variance is doubled. For this question you may find the xic 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 = = (a) If the null hypothesis is that there is no interference, write down Ho and HA in terms of possible values of where Y" N(0,2). [4] (b) Design a level a= 0.05 test to decide between Ho and HẠ, using the pivot approach. i.e. find k such that you reject Ho when Ý > K. Hint: Start by calculating a = PlÝ > K|Ho) and use the fact that I xã when y? yid N(0, 02). [7] (C) Find the probability B of concluding the interference is absent when it is in fact present. [5] (d) If you observe y = 2, is there enough evidence to reject Ho at significance level a = 0.01? [4] (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] =
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