5 (15) Short Questions (Show all work) (a) (3) The melting point of each of 16 samples of a certain brand of hydrogenated oil was determined resulting in X = 94.32. Assume that the distribution of the melting point is normal with a = 1.20. We test the hypothesis Họ: µ = 95 vs Ho: µ # 95. If a significance level of 0.10 is used, that if the probability of not concluding that true average melting point is different from 95, when the actual average melting point is 94. (Clearly first write down the formula to calculate the same and then calculate)

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5 (15) Short Questions (Show all work)
(a) (3) The melting point of each of 16 samples of a certain brand of
hydrogenated oil was determined resulting in X = 94.32. Assume that the
distribution of the melting point is normal with o = 1.20. We test the hypothesis
Họ: µ = 95 vs Ho: µ± 95. If a significance level of 0.10 is used, that if the
probability of not concluding that true average melting point is different from 95,
when the actual average melting point is 94.
(Clearly first write down the formula to calculate the same and then calculate)
3
(b) (2) A test of H0: µ = 0 versus Ha: µ > 0 is conducted on the same population
independently by two different researchers. They both use the same sample size
and the same value of a = 0.05.What will be the same for both researchers? (The
value of the test statistic/ the p-value of the test/ the power of the test if the true u
= 6/ decision about whether to reject or not to reject the Null Hypothesis).
(c) (3) If X, is a normal variate with mean 2 and standard deviation 4 and X2 is a
normal variate with mean 3 and standard deviation 9, then find EEX1 – 3X2 and
Var x1– 3X2
Transcribed Image Text:5 (15) Short Questions (Show all work) (a) (3) The melting point of each of 16 samples of a certain brand of hydrogenated oil was determined resulting in X = 94.32. Assume that the distribution of the melting point is normal with o = 1.20. We test the hypothesis Họ: µ = 95 vs Ho: µ± 95. If a significance level of 0.10 is used, that if the probability of not concluding that true average melting point is different from 95, when the actual average melting point is 94. (Clearly first write down the formula to calculate the same and then calculate) 3 (b) (2) A test of H0: µ = 0 versus Ha: µ > 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of a = 0.05.What will be the same for both researchers? (The value of the test statistic/ the p-value of the test/ the power of the test if the true u = 6/ decision about whether to reject or not to reject the Null Hypothesis). (c) (3) If X, is a normal variate with mean 2 and standard deviation 4 and X2 is a normal variate with mean 3 and standard deviation 9, then find EEX1 – 3X2 and Var x1– 3X2
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