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Concept explainers
Sampling Methods: Benefits Package An important part of employee compensation isa benefits package, which might include health insurance, life insurance. child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefits packages available in private businesses in Hawaii. You want a
(a) Assign each business in the Island Business Directory a number, and then use a random-number table to select the businesses to be included in the sample.
(b) Use postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP Code areas, and then include all the businesses in each selected ZIP Code area.
(c) Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block or building and interview an employee from each business found. Bach researcher can have the rest of the day off after getting responses from 20 different businesses.
(d) Use the Island Business Directory. Number all the businesses. Select a starting place at random, and then use every 50th business listed until you have 100 businesses.
(e) Group the businesses according to type: medical, shipping, retail, manufacturing, financial, construction, restaurant, hotel, tourism, other. Then select a random sample of 10 businesses from each business type.
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Chapter 1 Solutions
Bundle: Understanding Basic Statistics, Loose-leaf Version, 7th + WebAssign Printed Access Card for Brase/Brase's Understanding Basic Statistics, ... for Peck's Statistics: Learning from Data
- 2 (VaR and ES) Suppose X1 are independent. Prove that ~ Unif[-0.5, 0.5] and X2 VaRa (X1X2) < VaRa(X1) + VaRa (X2). ~ Unif[-0.5, 0.5]arrow_forward8 (Correlation and Diversification) Assume we have two stocks, A and B, show that a particular combination of the two stocks produce a risk-free portfolio when the correlation between the return of A and B is -1.arrow_forward9 (Portfolio allocation) Suppose R₁ and R2 are returns of 2 assets and with expected return and variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find −∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest risk.arrow_forward
- 7 (Multivariate random variable) Suppose X, €1, €2, €3 are IID N(0, 1) and Y2 Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3. = (In models like this, X is called the common factors of Y₁, Y₂, Y3.) Y = (Y1, Y2, Y3). (a) Find E(Y) and cov(Y). (b) What can you observe from cov(Y). Writearrow_forward1 (VaR and ES) Suppose X ~ f(x) with 1+x, if 0> x > −1 f(x) = 1−x if 1 x > 0 Find VaRo.05 (X) and ES0.05 (X).arrow_forwardJoy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways arrow_forward
- Solve for X. Explain each step. 2^2x • 2^-4=8arrow_forwardOne hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. Female (F) Male (F′) Total College degree (D) 30 20 50 No college degree (D′) 30 20 50 Total 60 40 100 If a person is selected at random from those surveyed, find the probability of each of the following events.1. The person is female or has a college degree. Answer: equation editor Equation Editor 2. The person is male or does not have a college degree. Answer: equation editor Equation Editor 3. The person is female or does not have a college degree.arrow_forwardneed help with part barrow_forward
- Suppose you know that Bob's test score is above the mean, but he doesn't remember by how much. At least how many students must score lower than Bob?arrow_forwardIf a baby's weight is at the median, what's her percentile?arrow_forwardAt the same restaurant as in Question 19 with the same normal distribution, what's the chance of it taking no more than 15 minutes to get service?arrow_forward
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