Exercise 5. Assume that we have observed the following values from a normal distribution withknown variance o2 = and unknown mean .1.23 -0.67 1.16 1.67 0.24 2.99 0.02 ..17 0.27 ..21.5%.Test the hypothesis Ho: = 0 against the alternative H₁: 0 at significance level a =Exercise 6. Let 0> 0 and XU[0,0], i.e. X is uniformly distributed on the interval [0,0].a) As a function of 0, determine P(X ≤ 1).b) Assume that is unknown, but we can observe X. For given 00, we want to test thehypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejectsHo, if and only if X < c. How should we choose c, as a function of 00 and a, to get a testwith significance level a? Carefully justify your answer.

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Answered: Exercise 5. Assume that we have…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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A large chemistry course took their final exam. The mean was 75 with a standard deviation of 8. What are the exam scores that separate the top and bottom 5 percent of the class (extreme 10%) 2. What are the exams scores that separate the middle 10% of the class (5% on each side of the mean)? Use table below and draw normal distribution
Calculate the standard deviation and variance of the sample data shown, to two decimal places 19.4 9.9 24.8 11.8 16.1 7.5 Standard deviation: Variance: Question Help: OVideo Check Answer here to search F3 F4 F5 F6 F7 F8 F9 F1 @ %23 & 3 4. 7 8. W T Y U S G * CO 本 Cl LL 吉

A researcher takes sample temperatures in Fahrenheit of 17 days from New York City and 18 days from Phoenix. Test the claim that the mean temperature in New York City is different from the mean temperature in Phoenix. Use a significance level of α=0.05. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. New York City Phoenix 99 94.2 95.5 72 93.2 86.8 102 122.1 85.4 114.4 80 94.7 86.4 89.7 75.4 104.7 79.5 77.6 83.4 106.8 64.3 98.6 65.5 91.5 87.7 82 104 97.7 74.3 64.9 59.5 82 82.8 72 116.2 The Hypotheses for this problem are: H0: μ1 = μ2 H1: μ1μ2 Find the p-value. Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. p-value =
The data in the table are from two normal distributions with the same mean and unequal variances. Treatment 1 21.9 20.2 19.4 20.3 19.6 20.4 18.4 20.1 22.0 18.9 Treatment 2 20.2 13.8 21.8 19.2 19.6 25.5 17.0 17.6 19.5 22.2 Test for differences between the two treatments using the Kolmogorov-Smirnoff test.
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Exercise 5. Assume that we have observed the following values from a normal distribution with known variance o2 = and unknown mean . 1.23 -0.67 1.16 1.67 0.24 2.99 0.02 ..17 0.27 ..21. Test the hypothesis Fo: = 0 against the alternative H₁: 0 at significance level a = 5%.