Econ True false
It is not possible to obtain a SRS unless you sample with replacement from the same population.
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It must always be the case that error terms drawn from normal with mean 0 and variance of population variance in order for t-statistics to provide valid inferences on the population intercept and slopes in the multivariate regression model. ( 4 PQ2)
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Let f(x) represent the pdf of a normally distributed random variable, X. f(x) represents the probability that X=x.( 2 PQ2)
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Like the sample correlation coefficient, rxy, the least squares slope, b2, provides information about the strength of the linear relationship between X and Y. (Final)
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Lower confidence levels yield wider confidence intervals. ( 3 PQ3)
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Panel data are data on different individuals collected at a given point in time. ( 1 PQ2)
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Simple random samples always produce statistics that are unbiased estimates of population parameters. ( 1 PQ3)
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Suppose that event A is "it rains in London tomorrow" and event B is "the Dartmouth baseball team wins its next home game." A and B are mutually exclusive. ( 2 PQ2)
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Suppose that the relationship between X and Y is statistically significant. This means that X causes Y. ( 4 PQ1)
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Suppose that two random variables X and Y are such that E(XY)=0. This implies that there is no linear population relationship between X and Y. ( 2 PQ4)
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Suppose that you have a simple random sample of 15 observations on some continuous variable X. Then x bar is drawn from a normal with mean mu x and standard error (variance divided by n) and you can proceed to use tstatistics to conduct statistical inference. ( 3 PQ3)
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The hypothesis test of no difference in means cannot be performed when Y is a dummy variable. ( 3 PQ2)
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The national time use survey was a random sample of US households asking how much time each member of the household spent on a variety of activities (working, cooking, cleaning, etc.) in a particular week. These data are time-series data. ( 1 PQ1)
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The probability of a Type I error falls when the number of observations in a simple random sample increases. ( 3 PQ3)
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We say that x is an "unbiased" estimator of because the sampling distribution of x becomes more tightly concentrated around the population mean as n increases. ( 1 PQ2)
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When two variables have a correlation coefficient of -1, a one-unit increase in x is associated with a one-unit decrease in y. ( 1 PQ4)
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X is a random variable. Then E(X2 ) = (E(X))2 . (Final)
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X is a random variable. Then E(X2 ) = (E(X))2 ( 2 PQ2)
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You draw a SRS of 100 households and obtain data on the wages of the household head and his or her partner, indinc1 and indinc2. You then calculate a new variable for household income hhinc = indinc1 +indinc2. It will be the case that hhinc = indinc1 + indinc2 and s^2 hhinc = s^2indinc1 + s^2indinc2
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You flip a fair coin 100 times and record the fraction of times that it comes up tails. The mean of the sampling distribution of this fraction is 0.5 and the standard deviation is 0.05. You have a 0.3% chance of getting a fraction tails below 0.35. ( 1 PQ4)
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You mix up your formulas and estimate mu X with x tilda = 1/(n-1) summation from 1 to n of X1) in a SRS. X tilda is an unbiased estimator of mu x ( 3 PQ2)
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You are more likely to reject H0 : mu X = mu 0 in favor of a two-sided alternative at any level of significance when X is lower variance. ( 3 PQ3)
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You ask a simple random sample of 100 individuals about their employment status. You record the results as follows: X=1 if employed, X=0 if not employed. The number of individuals employed in your sample is drawn from a binomial distribution. ( 2 PQ2)
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You have defined two dummy variables in a cross-sectional data set: femalei =1 if observation i is female, 0 if i is male, and malei =1 if i is male, 0 if i if female. female and male are mutually exclusive variables. (Final)
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You sometimes reject the null hypothesis in a two-sided test when you would fail to reject the same null hypothesis in a one-sided test at the same level of significance. ( 3 PQ1)
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f two random variables X and Y are independent, then the population slope, β1, is zero. ( 2 PQ1)
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Consider two variables, x and y. A higher sample correlation coefficient between x and y implies a lower error sum of squares (SSE). ( 1 PQ1)
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If X is a continuous random variable, then P(X=x)=0. ( 2 PQ4)
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If X is drawn from a normal distribution with mean 5 and variance 4, then P(X>9) roughly 2.5%. ( 2 PQ1)
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If X1 and X2 are i.i.d Bernoulli random variables then E(Xbar) = p and var(Xbar) = p(1-p)/2 where p represents the population mean of each X1 and X2
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If Y is a continuous random variable, then P(Y=y) = 0
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If a researcher adds another explanatory variable, X2i , to the bivariate model Yi = Beta nought + beta1X1 + error term and x1 and X2 are highly correlated, se b1 may rise. ( 4 PQ3)
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If the sample correlation coefficient is -1, then all (x, y) pairs in sample would lie along the same downward-sloping line. (Final)
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If two random variables X and Y are independent, then it is necessarily the case that cov(X,Y)=0. ( 2 PQ1)
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If two variables are linearly related, then R2 must be non-zero. ( 1 PQ4)
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If you have a simple random sample, then X bar is an unbiased, consistent, and efficient estimator of the population mean
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In an experiment, it should be the case by design that Expectation of error term conditional on X1 = 0 ( 4 PQ1)
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A natural experiment is a situation where the researcher manipulates which individuals receive the treatment. ( 1 PQ2)
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A researcher is interested in analyzing the variable z = x + y. If x and y are not linearly related, then Sz = Sx +Sy ( 1 PQ4)
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All else constant, the least squares slope estimator in a bivariate model, b1 , is more reliably estimated when values of the explanatory variable, x , are more concentrated around x bar . ( 4 PQ1)
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Having a simple random sample of size n is enough to ensure that x bar is drawn from a normal with population mean and population variance divided by n( 2 PQ4)
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If a least squares regression of y on x has a low model sum of squares relative to its total sum of squares, there is at best a weak causal effect of x on y. ( 1 PQ3)
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Two random variables that don't have a linear relationship are necessarily independent
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Two variables that have a sample correlation coefficient of zero have no relationship.
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You and another student are working together on a research project. You are frustrated to find that the slope estimates from your regressions are small and statistically insignificant. This means that there is not a causal relationship between the variables of interest. (Final)
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You can safely use a t-statistic when the variance of X is unknown and n<30, provided that you have a simple random sample.( 3 PQ2)
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. We say that an estimator is efficient if on average, across repeated random samples of size n, it takes on the value of the population parameter of interest. ( 3 PQ1)
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. For ordinary least squares estimators to be "BLUE," it must be the case that Error terms are independent for all i does not equal j ( 4 PQ3)
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. We have a random sample when selection into the sample occurs by chance rather than by choice. ( 1 PQ4)
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According to the least squares line ˆy = 0.2 + 34 ln x , a 1 percent increase in x is, on average, associated with a 0.34 unit change in y. (Final)
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Suppose that X1, X2, and X3 are independent random variables drawn from the same distribution, with mean mu X and variance sigma x all squared . Define a weighted average of these random variables as W = 1/4 x1 +1/2 x2 + 1/4 x3. It is the case that E(W) = mu x and Var(W) = 3/8 variance ( 2 PQ4)
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Suppose we reject the null hypothesis that 0 0 H : : mu x = mu nought in favor of the alternative Ha : mu X < mu 0 . It is possible that the difference between x bar and mu0 is statistically significant, but not economically significant. ( 3 PQ1)
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Increasing the size of a random sample by a factor of three makes standard errors three times smaller. (Final)
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A and B are mutually exclusive events. This is equivalent to saying that A and B are independent. ( 2 PQ1)
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If ln(x) and y are perfectly negatively correlated, then then a 1% increase in x is associated with a 1/100 unit decrease in y. ( 1 PQ3)
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If the error terms in a multivariate regression are heteroskedastic, then the OLS estimates of the slope parameters are biased
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If two variables are correlated, then either the first has a causal effect on the second or the second has a causal effect on the first. ( 1 PQ1)
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In a linear regression of ln y on x, the least squares slope gives the percentage change in y with a one-unit increase in x. ( 1 PQ2)
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In a simple random sample, each observation on a variable is drawn with replacement from a normal distribution with mean μ and variance σ2 ( 1 PQ1) .
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Including dummy variables for all values of a categorical variable in a multivariate regression creates a problem called heteroskedasticity. ( 4 PQ3)
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The standard error of the sample mean is an estimate of the standard deviation of the random variable X bar . ( 2 PQ2)
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The use of z-statistics and t-statistics to conduct statistical inference would not be appropriate if you did not have a simple random sample. ( 3 PQ1)
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Two variables can be perfectly dependent but have no linear association. ( 1 PQ3)
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All else constant, an increase in R2 will make it more likely that a researcher will conclude that the least squares slope in a bivariate model is statistically significant. ( 4 PQ2)
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All else constant, an increase in sample size will make it more likely for a researcher to conclude that the least squares slope in a bivariate model is statistically significant. ( 4 PQ3)
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All else constant, having an equal number of study participants in the treatment group and the control group of an experiment minimizes the standard error of b1, thus increasing the chances of finding a statistically significant treatment effect.
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As long as a simple random sample is drawn from the population of interest, it should be the case that the sample mean of X is an unbiased and consistent estimator of the population mean of X. ( 2 PQ3)
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For a given significance level, the p-value is enough information to tell you whether you reject the null hypothesis or not. (Final)
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If E[e1 | X1] = 0 in the simple linear regression model, then b1 can be interpreted as a causal estimate of the impact of X on Y
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If events A and B are mutually exclusive, then P(B|A)=0. ( 2 PQ4)
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If the median is larger than the mean, then the data are left-skewed. ( 1 PQ2)
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If you have a SRS and random assignment of dummy independent variable x, then the difference in the mean dependent variables between the treatment group and the control group (ybarx=1 - ybarx=0) is an unbiased estimator of the effect of x on y
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In a sufficiently large sample, hypothesis testing in the multiple regression model does not require us to assume that the errors are normally distributed.(Final)
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In a two-sided hypothesis test, the probability of rejecting a false null hypothesis is higher when the (true) alternative is further away from the hypothesized value. ( 3 PQ2)
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In approximately 95 percent of simple random samples with n ≥ 30, the sample mean of random variable X will be on the interval +/- two standard errors away from the mean( 2 PQ3)
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Including dummy variables for all values of a categorical variable in a multivariate regression creates a problem called perfect multicollinearity
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It is possible for two variables to be related even if their covariance is zero
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M&Ms are produced on an assembly line and dumped by machine into a large container. A single worker then scoops M&Ms into bags that are sold to consumers. Though workers are pretty careful, approximately 10% of M&Ms are broken by the time they reach consumers. The probability that at least 1 in 5 randomly drawn M&Ms will be broken is approximately 41 percent. ( 2 PQ3)
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Multivariate data can be cross-sectional, time-series, or panel data. ( 1 PQ3)
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Polynomial terms in X are useful to include in a multivariate model when you anticipate that the relationship between X and Y is non-linear. ( 4 PQ2)
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R2 always rises when you add explanatory variables in a multivariate regression model. ( 4 PQ2)
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Regardless of whether a test is one-sided or two-sided, you reject a null hypothesis at the 0.05 level of significance if the p-value is less than or equal to 0.05. ( 3 PQ1)
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Suppose that A and B are events, and P(A)=0.37, P(B)=0.10, and P(A|B)=0.74. Then P(B|A)=0.2. ( 2 PQ3)
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Suppose that X and Y are both Bernoulli random variables and that P(Y=0|X=1) = 0.4. The expected value of Y given that X=1 is 0.6. ( 2 PQ1)
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Suppose that X ~ N(10,100). Then F(10) = 0.5 , where F(. ) represents the cumulative distribution function of X. ( 2 PQ3)
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The chance of a Type I error is under the direct control of the researcher. (Final)
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The coefficient of variation is a unit-free measure of dispersion. (Final)
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The correlation coefficient conveys more information about a bivariate relationship than R^2
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The covariance and the correlation between the same two variables always have the same sign. ( 1 PQ2)
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The critical values for an upper one-sided hypothesis test are always positive. ( 3 PQ3)
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The distribution of the sample mean becomes less dispersed as the sample size( 1 PQ1) grows.
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The least squares estimators solve the problem minimization of error terms ( 4 PQ1)
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The least squares intercept and slope minimize the error sum of squares. ( 1 PQ3)
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The least squares slope in a bivariate regression is more precisely estimated when R2 is bigger, all else constant. (Final)
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The probability of a Type I error increases when alpha increases. ( 3 PQ2)
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