(a) Prove that if x is a positive real number and k is a nonnegative integer such that 2 k − 1 < x ≤ 2 k , then ⌈ log 2 x ⌉ = k .

Question

= Consider the hypothesis test Ho: μ₁ = μ₂ against H₁ μ₁ μ2. Suppose that sample sizes are n₁ = 15 and n₂ = 15, that x1 = 4.7 and X2 = 7.8 and that s² = 4 and s² = 6.26. Assume that o and that the data are drawn from normal distributions. Use απ 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ẞ = 0.05 if the true difference in means is - 2? Assume that α = 0.05. (a) The null hypothesis is 98.7654). rejected. The P-value is 0.0008 (b) The power is 0.94 . Round your answer to four decimal places (e.g. Round your answer to two decimal places (e.g. 98.76). (c) n₁ = n2 = 1 . Round your answer to the nearest integer.

Answer 1

Question

Chapter 11.4, Problem 14ES

To determine

(a)

Prove that if x is a positive real number and k is a nonnegative integer such that 2k−1<x≤2k, then ⌈log2x⌉=k.

To determine

(b)

Describe in words the statement proved in part (a).

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