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(b) Consider two populations. The first population has mean µ₁ and vari- ance of and the second has mean µ₂ and variance σ². We wish to test the hypothe- ses: H₁ : µ₁ − µ₂ = 0 vs H₁ : µ₁ − µ2 = 0.3 at the α = 5% significance level. Suppose we take two random samples from these distributions and as a result we have sample information: Do the following questions. İ. 2 ii. ⠀ n₁ = 42, x₁ = 0.39, $₁ = 0.37 n₂ = 51, x₂ = 0.18, $₂ = € 0.28. V. i- State the distributions of X₁, X₂ and X₁ — X₂. Explain why the test statistic is approximately normally distributed: X₁ – X₂ − (µ₁ − µ₂) /s²/n₁+s²/1₂ Z = N(0,1). Student ID: iii. { Do the test of hypothesis of Hå versus H₁. [(i) State the distribution of the test statistic under Họ. (ii) Calculate the observed value of the test statistic. (iii) Find the rejection region. (iv) Give a conclusion of the test.] iv. ! Find the p-value of the test. Find the power of the test.

(b) Consider two populations. The first population has mean µ₁ and vari- ance of and the second has mean µ₂ and variance σ². We wish to test the hypothe- ses: H₁ : µ₁ − µ₂ = 0 vs H₁ : µ₁ − µ2 = 0.3 at the α = 5% significance level. Suppose we take two random samples from these distributions and as a result we have sample information: Do the following questions. İ. 2 ii. ⠀ n₁ = 42, x₁ = 0.39, $₁ = 0.37 n₂ = 51, x₂ = 0.18, $₂ = € 0.28. V. i- State the distributions of X₁, X₂ and X₁ — X₂. Explain why the test statistic is approximately normally distributed: X₁ – X₂ − (µ₁ − µ₂) /s²/n₁+s²/1₂ Z = N(0,1). Student ID: iii. { Do the test of hypothesis of Hå versus H₁. [(i) State the distribution of the test statistic under Họ. (ii) Calculate the observed value of the test statistic. (iii) Find the rejection region. (iv) Give a conclusion of the test.] iv. ! Find the p-value of the test. Find the power of the test.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(b) Consider two populations. The first population has mean μ₁ and vari- ance of and the second has mean µ2 and variance 2. We wish to test the hypothe- ses: Hoμ₁₂0 vs H₁ μ₁ −μ₂ = 0.3 at the a = 5% significance level. Suppose we take two random samples from these distributions and as a result we have sample information: Do the following questions. İ. S ii. . V. i- = n₁ = 42, x₁ 0.39, $1 = 0.37 n₂ = 51, x₂ = 0.18, s₂ = 0.28. Z = = State the distributions of X₁, X₂ and X₁ – X₂. Explain why the test statistic is approximately normally distributed: - X₁ – X₂ – (µ₁ − µ₂) √/s²/n₁ + $ ²2/1₂ N(0,1). Student ID: iii. Do the test of hypothesis of Ho versus H₁. [(i) State the distribution of the test statistic under Ho. (ii) Calculate the observed value of the test statistic. (iii) Find the rejection region. (iv) Give a conclusion of the test.] iv. ! Find the p-value of the test. Find the power of the test.
Transcribed Image Text:(b) Consider two populations. The first population has mean μ₁ and vari- ance of and the second has mean µ2 and variance 2. We wish to test the hypothe- ses: Hoμ₁₂0 vs H₁ μ₁ −μ₂ = 0.3 at the a = 5% significance level. Suppose we take two random samples from these distributions and as a result we have sample information: Do the following questions. İ. S ii. . V. i- = n₁ = 42, x₁ 0.39, $1 = 0.37 n₂ = 51, x₂ = 0.18, s₂ = 0.28. Z = = State the distributions of X₁, X₂ and X₁ – X₂. Explain why the test statistic is approximately normally distributed: - X₁ – X₂ – (µ₁ − µ₂) √/s²/n₁ + $ ²2/1₂ N(0,1). Student ID: iii. Do the test of hypothesis of Ho versus H₁. [(i) State the distribution of the test statistic under Ho. (ii) Calculate the observed value of the test statistic. (iii) Find the rejection region. (iv) Give a conclusion of the test.] iv. ! Find the p-value of the test. Find the power of the test.
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