5________________________ 1) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) .0122 B) .8821 C) .8944 D) .4878 P(-2.25 < z < 1.25) = F(1.25) - (1 - F(2.25)) = 0.89435 - (1 - 0.987776) = 0.882126 2) Before a new phone system was installed‚ the amount a company spent on personal calls followed a normal distribution with an average of $ 900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE’s (personal call expenses). Using the distribution above‚ a. what is the probability
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Sampling Distributions Sampling Error = x̄ - μ Z-Values for a sampling distribution of x̄ : Z = Z-Values adjusted with Finite Population Correction Applied if: the sample is large relative to the population (n is greater than 5% of N) and sampling Is without replacement Z = Using the Sampling Distribution for Means Compute the Sample Mean Define the sampling distribution μx̄ = Define the probability statement of interest P(z30 will give sampling distribution that is nearly normal fairly
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deviation of any normal random variable is always equal to one. Answer: False Type: Concept Difficulty: Easy 2. For any normal random variable‚ the probability that the random variable will equal one is always zero. Answer: True Type: Concept Difficulty: Medium 3. The graph of a standard normal random variable is always symmetric. Answer: True Type: Concept Difficulty: Easy 4. The formula will convert any normal distribution into the “standard normal distribution
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Deviation σ = 24.24 s The fraction of days when hold time exceeded 110 s = P(x>110) =? Mean of a distribution (μ) and a data point (x) is related by the following equation: x = μ ± zσ For x > 110 s; XY Value of XY is area under normal curve between z = 0 to z = 0.43. Thus‚ approximately 1/3 or 0.336of days the call center failed to meet the targeted hold time. On the frequency distribution table this fraction is represented as 240/731 = approximately 1/3. -----------------------------
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Describing the Distribution of a Single Variable and Finding Relationships among variables Mean Formula Excel Function: = AVERAGE Coefficient of Variation: Standard Deviation / Mean Standard Deviation: square root of variance Sample Variance Population Variance Excel Function: Variance = VAR Standard Deviation = STDEV Mean Absolute Deviation Covariance Correlation Excel Function: =CORREL Chapter 4: Probability and Probability Distributions Conditional
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Tdistributions-test to see if variable A = variable B interval/ratio data/normal curve either they = each other or they do not-Mean of A/ Mean of B 2 tailed test is easier but yields less information than 1 tail Explanatory variable-explaining variable Week 3 Quiz Chapters 4‚ 5‚ 6 Study Reading from Week 2 Standard Deviation convert to percentages Normal Distribution? Rule for normal distribution. (MEMORIZE) Chapter 5 Normal distribution illustrating the 68%-95%-99.7% About 68% of the values fall
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The linear probability model‚ ctd. When Y is binary‚ the linear regression model Yi = β0 + β1Xi + ui is called the linear probability model. • The predicted value is a probability: • E(Y|X=x) = Pr(Y=1|X=x) = prob. that Y = 1 given x • Yˆ = the predicted probability that Yi = 1‚ given X • β1 = change in probability that Y = 1 for a given ∆x: Pr(Y = 1 | X = x + ∆x ) − Pr(Y = 1 | X = x ) β1 = ∆x 5 Example: linear probability model‚ HMDA data Mortgage denial v. ratio of debt payments to income (P/I
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discrete probability distribution. 10. Given E(X) = 0.55‚ Var(X) = 1.55 and Y = 2X + 1. Find E(Y) and Var(Y). 11. Show that the mean of the binomial distribution (q + p)2 is 2p. 12. Show that mean is 2p and σ2 = 2pq for a binomial distribution in which n = 2. 13. A random variable X has a binomial distribution with E(X) = 2.4 and p = 0.3. Find the standard deviation of X. 14. Describe the normal distribution and write down its equation. 15. What is standard normal variable? 16
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LEAD 6341 Research Methods and Statistics Midterm Exam Part II: Conceptual Problems (Open Book) Spring‚ 2013 1) Very briefly discuss the history of ethical problems in research in the US. Describe how current research policies and practices reduce the likelihood of ethical problems arising from research today. The Tuskegee study is an example of ethical problem in research in the US. The black subjects were promised medical care‚ meals‚ and burial insurance for their participation in
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the MM207 Student Data Set: a) Select a continuous variable that you suspect would not follow a normal distribution. b) Create a graph for the variable you have selected to show its distribution. c) Explain why these data might not be normally distributed. d) Select a second continuous variable that you believe would approximate a normal distribution e) Create a graph to show its distribution. f) Explain why these data might be normally distributed. . 3. Jonathan is a 42 year old male
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