Explain why the OLS estimator for the following model is inconsistent if random errors are serially correlated of order 1.

Q: Consider a standard model with a random sample of n observations from a population with a proportion…

A: The given test is two proportions test.

Q: An estimator for parameter v is consistent if E(v) is close to v when sample size is increased.…

A: Given If E(v) is close to parameter v, the estimator is consistent.

Q: Assume them to be a random sample from a normal population. Perform a hypothesis test at alpha =…

A: It is given that Sample size n = 10 Level of significance = 0.05 Test is that whether the variance…

Q: Which of the following can cause OLS estimators to be biased? PLEASE EXPLAIN 1. Heteroscedasticity…

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Q: Why would you use a low alpha? To minimize the probability to make a Type I error To minimize the…

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Q: The following model estimates the effect of the return to education: wage = A + B, educ + Berper +…

A: In the given regression model, researchers have found that education level is usually misreported by…

Q: One sample with n =8 has a S2 = 6 and a second sample n = 8 scores has a S2 = 10.  If the pooled…

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Q: A soft-drink dispensing machine is said to be out of control if the variance of the contents exceeds…

A: Null hypothesis: H0:σ2≤1.15 Alternative hypothesis: H1:σ2>1.15 The value of the test statistic is…

Q: The bearing for any computer hard drive can be modeled as a random variable with mean 0.225 mm and…

A: Let X be random variable that bear hard drive for any computer.   We are given X~N(μ, σ2) with mean,…

Q: Explain the Covariance functions as applicable to random processes.

A: The autocovariance function CX(s,t) of a random process {X(t)} is a function of two times s and t.…

Q: What are the Other (HAC) heteroskedasticity- and autocorrelation-consistent estimators?

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Q: When does z test is said to be accurate?

A: A z-test is a statistical test used to determine whether two population means are different when the…

Q: A simple random sample of 100 men aged 25–34 averaged 70 inches in height, and had astandard…

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Q: In a recently conducted survey, workers reported driving an average of 36 miles one way on their…

A: Given Population mean = 36miles Population standard deviation =5

Q: A random variable that can be used of the gamma distribution is

A: Random variable can be α=4,β Mean and variance can be, E(X)=αβ=4βVar(X)=αβ2=4β2 Size of sample is…

Q: A production manager at a wall clock company wants to test their new wall clocks. The designer…

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Q: In an industrial setting, process steam has been found to be normally distributed with an average…

A: Given: The process steam in the industrial setting is normally distributed. The average value is…

Q: Suppose two random variables have standard deviations of 0.10 and 0.23, respectively. What does this…

A: Given : Standard deviation (s.d)  :            It is a measure of dispersion which measure the…

Q: What happens to ordinary least squares estimators if their variances of the residual not constant?

A: Given information: The regression output is given.

Q: An extensive study of a simple random sample (n = 400,000) of American elementary school students…

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Q: What distributional assumption must be met in order to use the Wilcoxon signed-rank test?

A: Solution: It is required to mention the distributional assumption that must be met in order to use…

Q: When the errors in a regression model have AR(1) serial correlation, why do the OLS standard errors…

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Q: If the sick leave time of employees in a firm in a month is normally distributed with a mean of 50…

A: This question is related to Distributions. The solution to the given question is explained below.

Q: Suppose Bob rolls a fair die 100 times and X = number of 1's he gets. What is the variance of X?

A: Given: n = 100 P( obtaining a 1 on die) = 1/6 = p X = number of 1's obtained

Q: A published statistic says that 3% of a certain population have height above 174cm. Suppose the…

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Q: A sporting goods manufacturer claims that the variance of the strength of a certain fishing line is…

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Q: What is the smallest alpha that you CAN reject the null hypothesis under when you have a p-value of…

A: The level of significance can be defined as the probability of rejecting the null hypothesis when it…

Q: Calculate Karl Pearson's coefficient of correla- tion and its probable error from the following data…

A: Let X denote the Value of imports Y denote the Value of exports.

Q: Which of the following can cause OLS estimators to be biased?(i) Heteroskedasticity.(ii) Omitting an…

A: Introduction: Heteroskedasticity is a situation in regression analysis, when the variability of the…

Q: I am doing a two tailed z test with a z statistic of 1.72, what is my p value?

A: It is given that there is a z-test for two-tailed and the test statistics value is 1.72.

Q: Suppose X is a random variable with a mean of 10 and a variance of 100. suppose Y is a random…

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Q: As the size of a simple random sample is increased, the standard error of the sample mean will…

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Q: A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly…

A: Given: A manufacturer of chocolate chips would like to know whether it's bag filling machine works…

Q: Suppose that you run a Regression Model and the Regression Coefficient for X has an associated…

A: regression coefficient for X is β here confidence level = 99% so significance level = 1%

Q: A pencil manufacturer claims that its pencils have lengths that are normally distributed with a mean…

A: From the provided information,

Q: Suppose the study described in the previous question was conducted by a colleague.  He tells you…

A: The null and alternative hypotheses are: Null hypothesis: The proportions are the same across health…

Q: Suppose that a random variable X is normally distributed with a mean of 200 and a variance of 625.…

A: We have given that a random variable X is normally distributed with a mean of 200 and a variance of…

Q: The critical value of t for a two-tailed test with 10 degrees of freedom using α = .05 is?

A: Given that, The test is a two-tailed test with 10 degrees of freedom using α = .05.

Q: Consider two independent samples — the first of size 10 from a normal population having variance 4…

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Q: Explain the following with respect to Random process, (1) Correlation ergodic processes

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Q: For a Poisson random variable, what is the relationship between its parameter and its mean?

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Q: In analyzing a patient admissions at a hospital, it is found that 31,469 patients were admitted in a…

A: Determine the standard deviation for the values of x. The standard deviation for the values of x is…

Q: 2- The variance can never be: a) Zero b) Smaller than the standard deviation

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Q: Suppose that having a widow's peak was a dominant trait (W) compared to not having a widow's peak…

A: Introduction: Denote p1 and p2 as the respective expected proportions of having a widow’s peak, and…

Q: For a random variable X with standard deviation 5, Variance of 2x + 4 is

A: It is given that, Standard deviation of X is 5 Now, The variance of X is =52=25

Q: The standard normal curve exhibits heavier tails versus the t-distribution curve  True  False

A: Let Z follows Std. Normal distribution i.e N(0, 1) And t follows t distribution.

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.