Exam Questions on Basic Statistics
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This document is a quiz examination for a statistics course consisting of 4 questions testing understanding of correlation, regression, interpreting correlation coefficients, and applying regression to a sample data set involving fertilizer amounts and rice production amounts. Students are asked to define correlation and regression, give examples of different correlation types, interpret provided correlation coefficients, calculate and interpret a correlation coefficient for sample data, fit a regression line to the sample data and use it to predict future values. The exam is worth a total of 100 marks and must be completed within 50 minutes.
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Exam Questions on Basic Statistics
Correlation examines the relationship between two variables, while regression seeks to quantify that relationship and predict future outcomes. Examples of correlation include fertilizer and rice production (positive), temperature and crime rates (negative), and family size and GPA (zero). Interpreting results, r=0.79 represents a strong positive correlation, r=-0.65 a moderate negative correlation, r=0.34 a weak positive correlation, and r=-0.18 a weak negative correlation. For rice production data, r=0.97 indicates a strong positive correlation, the regression line predicts higher production as fertilizer increases, and when X=10, Y would be predicted to be 20.
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The document discusses circuit resonance in a series RLC circuit. It shows that when the capacitive and inductive reactances are equal (XC = XL), the impedance of the circuit reaches its minimum and resonance occurs. At resonance, the current is in phase with the applied voltage. Away from resonance, the current leads or lags the voltage depending on whether the capacitive or inductive reactance is dominant. The document provides equations for the resistor, capacitor, and inductor currents as well as expressions for the amplitude of the current and the phase angle at different frequencies.
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The document discusses properties of fractions and inverse operations. It shows that the inverse of a fraction a/b is b/a through algebraic steps using the properties of fractions. It also states that the inverse of a composition of operations (α o β) is the composition of the inverses in reverse order (β-1 o α-1).
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1. The document discusses the "pizza problem" of dividing a circle into slices using chords and determining if the black and white areas are equal.
2. It introduces the Tiffany Lemma, which shows that the sum of the squares of the lengths of four chords through a point is a constant equal to 4 times the radius squared.
3. By using polar coordinates and the Tiffany Lemma, the solution shows that the integral of the black and white areas over any interval of length π/2 is π/2, proving the areas are equal.
Derivatives Table
This document provides tables of derivatives for common functions. It lists the derivatives of basic functions like constants, polynomials, logarithms and exponentials. It then gives derivatives of trigonometric functions like sine, cosine, tangent and cotangent. Finally, it provides derivatives of inverse trigonometric functions like arcsine, arccosine, arctangent and arccotangent.
Exam Questions on Basic Statistics
The document contains a 10 question quiz about measures of central tendency including mode, mean, median, harmonic mean, and examples of calculating and applying these concepts. Questions 1-3 ask about the definitions of mode, mean, and median; questions 4-5 involve calculating mode and re-calculating a mean. The remaining questions ask about criteria for good measures of central tendency, situations where mean and mode are not applicable, explaining harmonic mean with an example, and calculating mean and finding numbers with a given arithmetic and geometric mean.
Exam Questions on Basic Statistics
This document contains a midterm examination for a statistics course with 7 questions covering topics like:
- Calculating probabilities of coin tosses and dice rolls
- Probability distributions and calculating average, variance for family sizes
- Interpreting correlation coefficients
- Finding probabilities and expected values for vehicle passage rates
- Calculating probabilities and ranges for the standard normal distribution
- Finding the expected value and variance for a random variable with a given probability distribution
Exam Questions on Basic Statistics
Quiz #7 (A) contains 6 questions about probability and statistics concepts. Question 1 asks to define a random variable with an example. Question 2 asks to find the average family size and variance based on a given probability distribution for family size. Question 3 asks to find the expected value and variance of a random variable with a given probability density function. Question 4 asks to find the probability that 3 out of 5 randomly selected patients will recover given survival rate data. Question 5 asks to find the probability that a sample of 200 items will contain exactly 4 defective items given a known defect rate. Question 6 asks to find probabilities related to the standard normal distribution.
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Exam Questions on Basic Statistics
Correlation examines the relationship between two variables, while regression seeks to quantify that relationship and predict future outcomes. Examples of correlation include fertilizer and rice production (positive), temperature and crime rates (negative), and family size and GPA (zero). Interpreting results, r=0.79 represents a strong positive correlation, r=-0.65 a moderate negative correlation, r=0.34 a weak positive correlation, and r=-0.18 a weak negative correlation. For rice production data, r=0.97 indicates a strong positive correlation, the regression line predicts higher production as fertilizer increases, and when X=10, Y would be predicted to be 20.
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The document discusses circuit resonance in a series RLC circuit. It shows that when the capacitive and inductive reactances are equal (XC = XL), the impedance of the circuit reaches its minimum and resonance occurs. At resonance, the current is in phase with the applied voltage. Away from resonance, the current leads or lags the voltage depending on whether the capacitive or inductive reactance is dominant. The document provides equations for the resistor, capacitor, and inductor currents as well as expressions for the amplitude of the current and the phase angle at different frequencies.
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The document discusses properties of fractions and inverse operations. It shows that the inverse of a fraction a/b is b/a through algebraic steps using the properties of fractions. It also states that the inverse of a composition of operations (α o β) is the composition of the inverses in reverse order (β-1 o α-1).
Pizza Problem
1. The document discusses the "pizza problem" of dividing a circle into slices using chords and determining if the black and white areas are equal.
2. It introduces the Tiffany Lemma, which shows that the sum of the squares of the lengths of four chords through a point is a constant equal to 4 times the radius squared.
3. By using polar coordinates and the Tiffany Lemma, the solution shows that the integral of the black and white areas over any interval of length π/2 is π/2, proving the areas are equal.
Derivatives Table
This document provides tables of derivatives for common functions. It lists the derivatives of basic functions like constants, polynomials, logarithms and exponentials. It then gives derivatives of trigonometric functions like sine, cosine, tangent and cotangent. Finally, it provides derivatives of inverse trigonometric functions like arcsine, arccosine, arctangent and arccotangent.
Exam Questions on Basic Statistics
The document contains a 10 question quiz about measures of central tendency including mode, mean, median, harmonic mean, and examples of calculating and applying these concepts. Questions 1-3 ask about the definitions of mode, mean, and median; questions 4-5 involve calculating mode and re-calculating a mean. The remaining questions ask about criteria for good measures of central tendency, situations where mean and mode are not applicable, explaining harmonic mean with an example, and calculating mean and finding numbers with a given arithmetic and geometric mean.
Exam Questions on Basic Statistics
This document contains a midterm examination for a statistics course with 7 questions covering topics like:
- Calculating probabilities of coin tosses and dice rolls
- Probability distributions and calculating average, variance for family sizes
- Interpreting correlation coefficients
- Finding probabilities and expected values for vehicle passage rates
- Calculating probabilities and ranges for the standard normal distribution
- Finding the expected value and variance for a random variable with a given probability distribution
Exam Questions on Basic Statistics
Quiz #7 (A) contains 6 questions about probability and statistics concepts. Question 1 asks to define a random variable with an example. Question 2 asks to find the average family size and variance based on a given probability distribution for family size. Question 3 asks to find the expected value and variance of a random variable with a given probability density function. Question 4 asks to find the probability that 3 out of 5 randomly selected patients will recover given survival rate data. Question 5 asks to find the probability that a sample of 200 items will contain exactly 4 defective items given a known defect rate. Question 6 asks to find probabilities related to the standard normal distribution.
Exam Questions on Basic Statistics
This document is the first term examination for the course STA 240 at the International University of Business Agriculture and Technology. It consists of 10 multiple choice questions testing statistical concepts such as: constructing a line graph from monthly share index data; finding the mean, harmonic mean, geometric mean, variance, standard deviation, coefficient of variation, median, and constructing a stem-and-leaf plot for given data sets. The last question asks the student to find the median of a sample of numbers.
Exam Questions on Basic Statistics
This document contains a 10 question quiz for a statistics course. The quiz covers topics related to measures of central tendency including mean, median, mode, harmonic mean and geometric mean. Questions ask students to define and calculate these measures, as well as explain situations where some measures are not applicable or how extreme values can affect the mean. The quiz is worth a total of 100 marks and must be completed within 50 minutes.
Exam Questions on Basic Statistics
This document contains questions about different sampling methods used in statistics. It asks to list the advantages and disadvantages of simple random sampling, explain the lottery method with an example, outline the differences between stratified sampling and cluster sampling, and explain systematic sampling with an example.
Exam Questions on Basic Statistics
This document contains a 25 question final exam for a statistics course. The questions cover a range of statistical topics including: [1] classifying variables, [2] separating variables into discrete vs continuous categories, [3] identifying quantitative vs qualitative variables, [4] determining which measure of central tendency to use, [5] the effect of adding or multiplying values on measures of central tendency, and [6] probability questions related to sampling, distributions, and experiments. Students are asked to calculate measures like mean, variance, and probability in several multi-part questions testing their understanding of fundamental statistical concepts.
Exam Questions on Basic Statistics
The document is a midterm examination for a statistics course consisting of 6 questions testing concepts like probability, distributions, correlation, and hypothesis testing. The exam covers finding probabilities of coin tosses, determining values and measures from a probability distribution of family sizes, calculating the probability of patient recovery outcomes, and interpreting correlation coefficients. It is worth a total of 100 marks and must be completed within 50 minutes.
Exam Questions on Basic Statistics
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The document provides a class test with 7 questions about statistical concepts like coefficient of variation (CV), standard deviation (SD), mean, median, mode, variance, and measures of dispersion. It asks students to find the CV and SD for sets of numbers, determine a mean given the SD, and calculate statistical values like the geometric mean, harmonic mean, arithmetic mean, and variance for a pair of numbers when given the geometric mean and standard deviation. It also asks when CV should be used and which measure of dispersion is best.
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1. The document is the final examination for a statistics course with 16 questions covering topics such as measures of central tendency and dispersion, probability, sampling, distributions, correlation, and hypothesis testing.
2. Students are instructed to return the question paper along with their answer script after completing the 3 hour exam.
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This document contains a 10 question quiz on probability concepts. The quiz covers topics like finding the probability of choosing consonants from the alphabet, rolling odd numbers on a die, choosing letters from given sets of options, and drawing colored balls or marbles from bags/jars with specified contents. The quiz is being administered to students at the International University of Business Agriculture and Technology, is set Z, and is worth a total of 100 marks to be completed within 50 minutes.
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This document contains questions about different sampling methods used in statistics. It asks the reader to define random sampling and name four methods for drawing random samples, explain stratified sampling with an example, list the advantages and disadvantages of systematic random sampling, and explain cluster sampling with an example.
Exam Questions on Basic Statistics
This document appears to be a quiz for a statistics exam with 7 questions covering various statistical topics:
1. Properties of the Poisson distribution and normal distribution.
2. Definition of a random variable with an example.
3. Finding values for a probability distribution of family sizes including the value of m, the average family size, and the variance.
4. Calculating the expected value and variance for a given probability density function.
5. Finding the probability that 5 out of 10 randomly selected patients will recover from a disease where the probability of death is 25%.
6. Finding the probability that a sample of 500 electric motors will contain exactly 10 defective motors, given a 5% probability
Exam Questions on Basic Statistics
This document contains a practice exam for the course STA 240 with 13 questions testing statistical concepts. The exam covers topics like frequency tables, measures of dispersion, measures of central tendency, probability, correlation, and hypothesis testing. Students are asked to calculate statistics, define terms, explain concepts, and perform other analysis on data related to these statistical topics. The exam is out of 35 total marks and students have 2 hours to complete it.
Exam Questions on Basic Statistics
The document contains a 10 question quiz about measures of central tendency including the mean, median, and mode. Questions 1-3 ask about which measure is most affected by extreme values and the levels of measurement required for the median and mode. Questions 4-5 provide examples to calculate the median and mean. Questions 6-7 ask about the best measure of central tendency and situations where harmonic mean and geometric mean are not applicable. Questions 8-9 give examples to calculate the mean of series. Question 10 asks to explain the concept of geometric mean with an example.
Exam Questions on Basic Statistics
This document contains 18 questions about key concepts in statistics including: defining statistics and its applications; the concepts of variables, samples, populations, qualitative and quantitative variables, independent and dependent variables, scales of measurement; and how to construct various graphs like line graphs, histograms, stem-and-leaf plots, scatter diagrams; and how to classify different variables. It asks the student to apply these statistical concepts to various data sets and examples.
Exam Questions on Basic Statistics
This document contains instructions for a statistics exam with 7 questions. The questions include: constructing a frequency polygon from a table of class widths and frequencies; calculating the mean of 4 numbers given the mean of the 5 numbers and one value; finding the mean, median, and variance from various data sets; and calculating the arithmetic mean given the standard deviation and coefficient of variation.
Exam Questions on Basic Statistics
This document contains instructions for a statistics exam with 6 multiple choice questions. The questions include: constructing a histogram from frequency data; calculating mean when one value is known; finding the mean, median, and variance from data sets; and determining two numbers when their average and standard deviation are given. The exam is for the course STA 240 at IUBAT–INTERNATIONAL UNIVERSITY OF BUSINESS AGRICULTURE AND TECHNOLOGY.
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This document contains 35 multiple choice questions about correlation analysis. Correlation analysis measures the relationship between two variables and can be used to predict one variable based on the other. The correlation coefficient ranges from -1 to 1, with -1 indicating a perfect negative correlation and 1 indicating a perfect positive correlation. Questions cover topics like calculating the correlation coefficient from data, interpreting the direction and strength of correlation based on scatter plots, and the effects of transformations on the correlation coefficient.
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Exam Questions on Basic Statistics
This document is the first term examination for the course STA 240 at the International University of Business Agriculture and Technology. It consists of 10 multiple choice questions testing statistical concepts such as: constructing a line graph from monthly share index data; finding the mean, harmonic mean, geometric mean, variance, standard deviation, coefficient of variation, median, and constructing a stem-and-leaf plot for given data sets. The last question asks the student to find the median of a sample of numbers.
Exam Questions on Basic Statistics
This document contains a 10 question quiz for a statistics course. The quiz covers topics related to measures of central tendency including mean, median, mode, harmonic mean and geometric mean. Questions ask students to define and calculate these measures, as well as explain situations where some measures are not applicable or how extreme values can affect the mean. The quiz is worth a total of 100 marks and must be completed within 50 minutes.
Exam Questions on Basic Statistics
This document contains questions about different sampling methods used in statistics. It asks to list the advantages and disadvantages of simple random sampling, explain the lottery method with an example, outline the differences between stratified sampling and cluster sampling, and explain systematic sampling with an example.
Exam Questions on Basic Statistics
This document contains a 25 question final exam for a statistics course. The questions cover a range of statistical topics including: [1] classifying variables, [2] separating variables into discrete vs continuous categories, [3] identifying quantitative vs qualitative variables, [4] determining which measure of central tendency to use, [5] the effect of adding or multiplying values on measures of central tendency, and [6] probability questions related to sampling, distributions, and experiments. Students are asked to calculate measures like mean, variance, and probability in several multi-part questions testing their understanding of fundamental statistical concepts.
Exam Questions on Basic Statistics
The document is a midterm examination for a statistics course consisting of 6 questions testing concepts like probability, distributions, correlation, and hypothesis testing. The exam covers finding probabilities of coin tosses, determining values and measures from a probability distribution of family sizes, calculating the probability of patient recovery outcomes, and interpreting correlation coefficients. It is worth a total of 100 marks and must be completed within 50 minutes.
Exam Questions on Basic Statistics
This document appears to be a quiz examination for a statistics course consisting of 5 questions worth a total of 100 marks. The questions cover definitions of statistics and variables, applications of statistics, the concepts of sample and population with examples, and properties of different measurement scales with examples. The exam is 50 minutes long for the student to answer 5 questions ranging from 10 to 40 marks each.
Exam Questions on Basic Statistics
This document appears to be a quiz examination for a statistics course consisting of 7 multiple choice or short answer questions. The questions cover key topics in statistics sampling including different sampling methods such as simple random sampling, stratified sampling, cluster sampling, and systematic sampling. The examinee is asked to define these sampling techniques and provide examples of each. They are also asked to compare and contrast stratified sampling versus cluster sampling.
Exam Questions on Basic Statistics
This document contains a quiz examination for the course STA 240 with 7 multiple choice questions testing concepts related to measures of central tendency, dispersion, coefficient of variation, mean, standard deviation, median, geometric mean, harmonic mean, and mode. The quiz is out of 100 marks with 10 marks allocated to each question and an additional 30 marks. Students have 50 minutes to complete the quiz.
Exam Questions on Basic Statistics
The document contains 11 probability questions covering topics like choosing letters from the alphabet or a word, rolling dice, choosing marbles from a jar, and picking beads from a bag. The questions ask to calculate probabilities of specific outcomes like rolling an odd number, choosing a vowel letter, obtaining a head when tossing coins, and picking a yellow bead from a bag containing beads of different colors.
Exam Questions on Basic Statistics
This document contains an assignment with 13 questions related to statistics. The questions cover topics such as the definition of statistics, sources of data, frequency distribution, graphical representation of data, types of bar diagrams, measures of central tendency including arithmetic mean, geometric mean, harmonic mean, calculating mean from frequency distributions, constructing multiple and component bar diagrams, and finding mean, mode, and values to satisfy given arithmetic and geometric means.
Exam Questions on Basic Statistics
The document provides a class test with 7 questions about statistical concepts like coefficient of variation (CV), standard deviation (SD), mean, median, mode, variance, and measures of dispersion. It asks students to find the CV and SD for sets of numbers, determine a mean given the SD, and calculate statistical values like the geometric mean, harmonic mean, arithmetic mean, and variance for a pair of numbers when given the geometric mean and standard deviation. It also asks when CV should be used and which measure of dispersion is best.
Id
1. The document is the final examination for a statistics course with 16 questions covering topics such as measures of central tendency and dispersion, probability, sampling, distributions, correlation, and hypothesis testing.
2. Students are instructed to return the question paper along with their answer script after completing the 3 hour exam.
3. Formulas for measures like standard deviation, mean deviation, and correlation are provided to assist with calculations for questions requiring them.
Exam Questions on Basic Statistics
This document contains a 10 question quiz on probability concepts. The quiz covers topics like finding the probability of choosing consonants from the alphabet, rolling odd numbers on a die, choosing letters from given sets of options, and drawing colored balls or marbles from bags/jars with specified contents. The quiz is being administered to students at the International University of Business Agriculture and Technology, is set Z, and is worth a total of 100 marks to be completed within 50 minutes.
Exam Questions on Basic Statistics
This document contains questions about different sampling methods used in statistics. It asks the reader to define random sampling and name four methods for drawing random samples, explain stratified sampling with an example, list the advantages and disadvantages of systematic random sampling, and explain cluster sampling with an example.
Exam Questions on Basic Statistics
This document appears to be a quiz for a statistics exam with 7 questions covering various statistical topics:
1. Properties of the Poisson distribution and normal distribution.
2. Definition of a random variable with an example.
3. Finding values for a probability distribution of family sizes including the value of m, the average family size, and the variance.
4. Calculating the expected value and variance for a given probability density function.
5. Finding the probability that 5 out of 10 randomly selected patients will recover from a disease where the probability of death is 25%.
6. Finding the probability that a sample of 500 electric motors will contain exactly 10 defective motors, given a 5% probability
Exam Questions on Basic Statistics
This document contains a practice exam for the course STA 240 with 13 questions testing statistical concepts. The exam covers topics like frequency tables, measures of dispersion, measures of central tendency, probability, correlation, and hypothesis testing. Students are asked to calculate statistics, define terms, explain concepts, and perform other analysis on data related to these statistical topics. The exam is out of 35 total marks and students have 2 hours to complete it.
Exam Questions on Basic Statistics
The document contains a 10 question quiz about measures of central tendency including the mean, median, and mode. Questions 1-3 ask about which measure is most affected by extreme values and the levels of measurement required for the median and mode. Questions 4-5 provide examples to calculate the median and mean. Questions 6-7 ask about the best measure of central tendency and situations where harmonic mean and geometric mean are not applicable. Questions 8-9 give examples to calculate the mean of series. Question 10 asks to explain the concept of geometric mean with an example.
Exam Questions on Basic Statistics
This document contains 18 questions about key concepts in statistics including: defining statistics and its applications; the concepts of variables, samples, populations, qualitative and quantitative variables, independent and dependent variables, scales of measurement; and how to construct various graphs like line graphs, histograms, stem-and-leaf plots, scatter diagrams; and how to classify different variables. It asks the student to apply these statistical concepts to various data sets and examples.
Exam Questions on Basic Statistics
This document contains instructions for a statistics exam with 7 questions. The questions include: constructing a frequency polygon from a table of class widths and frequencies; calculating the mean of 4 numbers given the mean of the 5 numbers and one value; finding the mean, median, and variance from various data sets; and calculating the arithmetic mean given the standard deviation and coefficient of variation.
Exam Questions on Basic Statistics
This document contains instructions for a statistics exam with 6 multiple choice questions. The questions include: constructing a histogram from frequency data; calculating mean when one value is known; finding the mean, median, and variance from data sets; and determining two numbers when their average and standard deviation are given. The exam is for the course STA 240 at IUBAT–INTERNATIONAL UNIVERSITY OF BUSINESS AGRICULTURE AND TECHNOLOGY.
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Econ 103 Homework 2Manu NavjeevanAugust 15, 2022S
Econ 103: Homework 2
Manu Navjeevan
August 15, 2022
Single Linear Regression Theory Review
1. Recall that we define our parameters of interest β0 and β1 as the parameters governing the “line of
best fit” between Y and X:
β0,β1 = arg min
b0,b1
E[(Y − b0 − b1X)2]. (1)
Once we define these parameters we define the regression error term � = Y − β0 − β1X which then
generates the linear model
Y = β0 + β1X + �.
(a) Using the first order conditions for β0 and β1 (set the derivatives of the right hand side of (1)
with respect to b0 and b1 equal to zero at) show why E[�] = E[�X] = 0.
(b) Using the definition of β0 and β1 as line of best fit parameters, give an intuitive explanation for
why E[�] = 0.
Hypothesis Testing and Confidence Intervals
In the following questions, whenver running a hypothesis test, please state the null and alternative hypotheses,
show some work, and state the conclusion of the test.
1. In an estimated simple regression model based on n = 64, the estimated slope parameter, β̂1, is 0.310
and the standard error of β̂1 is 0.082.
(a) What is σ̂2β1 ? Recall σβ1 is the terms such that, approximately for large n,
√
n(β̂1 −β1) ∼ N(0,σβ1 ).
(b) Test the hypothesis that the slope is zero against the alternative that it is not at the 1% level of
significance (α = 0.01).
(c) Test the hypothesis that the slope is negative against the alternative that it is positive at the 1%
level of significance (α = 0.01).
(d) Test the hypothesis that the slope is positive against the alternative that it is negative at the 5%
level of significance. What is the p-value?
1
Page 2
(e) Generate a 99% confidence interval for β1. How can we use this interval to run the hypothesis
test in part (b)?
2. Consider a simple regression of log-income (income is measured thousands of dollars), Y , against years
of education, X. After collecting a sample of size n = 50 we estimate the following regression equation.
Ŷ = β̂0 + 0.0180X.
(a) Using the following information to solve for β̂0 as well as the estimated variance V̂ar(β̂0), which
is the square of the standard error.
• The standard error of β̂0 is 2.174
• The test statistic, t∗, associated with the hypothesis test for
H0 : β0 = 0 vs. H1 : β0 6= 0,
is equal to 1.257.
(b) Use the following information to solve for the standard error β̂1 as well as the estimated variance
V̂ar(β̂1), which is the square of the standard error.
• The test statistic, t∗, associated with the hypothesis test for
H0 : β1 = 0 vs. H1 : β1 6= 0,
is equal to 5.754
(c) Given that Y is a logged variable, Y = log(income), how do we interpret β̂1?
(d) Suppose that we are interested in the average value of log-income for someone with 16 years of
education. We want to use the model above to test the hypothesis that the average value of
log-income for someone with 16 years of education is less than or equal to 1.85. That is we want
to test
H0 : λ = β0 + 16β1 ≤ 1.85 vs. H1 : λ = β0 + 16β1 > 1.85.
Use the ...
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