Introduction to Statistics and Data Analysis
Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Chapter 12.1, Problem 1E

A particular cell phone case is available in a choice of four different colors. A store sells all four colors. To test the hypothesis that sales are equally divided among the four colors, a random sample of 100 purchases is identified.

  1. If the resulting X2 value were 6.4, what is the conclusion when using a test with significance level 0.05?
  2. What conclusion would be appropriate at significance level 0.01 if X2 = 15.3?
  3. If there were six different covers rather than just four, what is the conclusion if X2 = 13.7 and a test with α = 0.05 was used?
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1 (Expected Shortfall) Suppose the price of an asset Pt follows a normal random walk, i.e., Pt = Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²). Po+r1+. ⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price in T days, i.e., VaRq(Pt – Pt–T). - • If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution) Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47). What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3? What is P(rt (4) < 2)? What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13? • What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given rt-2 = 0.6?

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Introduction to Statistics and Data Analysis

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