Practice exams
A statistic is: A. a sample characteristic B. a population characteristic C. unknown D. normally distributed
A
The purpose of statistical inference is to provide information about the ____. a. population based on information within the sample b. sample based on information within the population c. population based on information within the population d. sample statistics based on information within the population parameters
A We want to know about the population, but it is too prohibitive to gather information about the entire population. So, we gather information about a sample and make inference about the population based on that sample.
Assuming a linear relationship between X and Y, which of the following is true if the estimated coefficient equals -0.30? A. There is no correlation. B. The slope (β1) is negative. C. Variable X is larger than variable Y. D. The variance of X is negative.
B
Which of the following best describes what 𝑹^𝟐 represents? a. The amount of variation in the dependent variable explained by the independent variables b. The amount of variation in the independent variables explained by the dependent variable c. The amount of variation in the dependent variable explained by the error term d. The amount of variation in the independent variables explained by the error term
A
Which of the following setups correspond to a negative, one-tailed hypothesis test? a. Ho: μ < 13 Ha: μ≥ 13 b. Ho: μ≥ 74.5 Ha: μ < 74.5 c. Ho: μ = 22 Ha: μ≠ 22 d. Ho: μ≤ 13 Ha: μ > 13
B One tailed test relates to testing whether the value is less than (<) or greater than (>). A negative one tailed test relates to whether value is less than. So our alternative hypothesis will be Ha: μ < 74.5 (Ho: μ≥ 74.5)
Using the Standard Normal Distribution, find the probability that Z > 1. a. 0.0158 b. 0.1587 c. 0.5000 d. 0.9500
B We know P (Z > 1) = 1 - P (Z ≤ 1). In the z-table we can find P (Z ≤ 1) = 0.8413. Thus, P (Z > 1) = 1 - P (Z ≤ 1) = 0.1587
Stratified random sampling is a method of selecting a sample in which _____. a. the sample is first divided into groups, and then random samples are taken from each group b. various strata are selected from the sample c. the population is first divided into groups, and then random samples are drawn from each group d. None of the answers is correct.
C
In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails.
TRUE
The letter Z is used to denote a random variable with any normal distribution.
TRUE
The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.
TRUE
If we fail to reject the null hypothesis (H0) that means that the test statistics was not in the rejection region. A. True B. False
A
Which of the following is not a correct way to state an alternative hypothesis? A. HA: μ = 0 B. HA: μ > 10 C. HA: μ < 0 D. HA: μ≠μ0
A
Parameters and statistics... A. Are both used to make inferences about Xbar. B Describe the population and the sample, respectively. C. Describe the sample and the population, respectively. D. Describe the same group of individuals.
B
The probability P (Z < −1.28) is closest to ________. a. −0.10 b. 0.10 c. 0.20 d. 0.90
B
What do residuals represent? A. The difference between the actual Y values and the mean of Y. B. The difference between the actual Y values and the predicted Y values. C. The square root of the slope. D. The predicted value of Y for the average X value.
B
What does the slope (β1) represent? A. The predicted value of Y when X = 0. B. The estimated change in average Y per unit change in X. C. The predicted value of Y. D. The variation around the line of regression.
B
What is the name of the variable that is used to predict another variable? a. Response b. Explanatory c. Coefficient of determination d. Standard error of the estimate
B
Which of the following are two-tailed tests? a. H0: μ≤ 10, HA: μ > 10 b. H0: μ = 10, HA: μ≠ 10 c. H0: μ≥ 400, HA: μ < 400 d. Both H0: μ≤ 10, HA: μ > 10 and H0: μ≥ 400, HA: μ < 400
B
A z-value of -1.83 represents: a. a corresponding x value that falls 1.83 standard deviations above the mean b. a corresponding x value that falls 1.83 standard deviations below the mean c. a corresponding x value that is 95% accurate d. a corresponding x value that is 99% accurate
B By definition the z-value represents how many standard deviations a value x is away from the mean. If z is negative it means the value is below the mean. So z = -1.83 means that the corresponding x value is 1.83 standard deviations below the mean.
Evaluate 𝑃(−1.1≤𝑍≤ 0.21) A. 0.1357 B. 0.4475 C. 0.5525 D. 0. 5832
B Find P(z>=1.1)=.1357 Find P (z<=0.21)=.5832 .5832-.1357 = .4475
A researcher has collected the following sample data. 5,12,6,8,5,6,7,5,12,4 The median is _____. a. 5 b. 6 c. 7 d. 8
B First: order the values from lowest to highest: 4 5 5 5 6 6 7 8 12 12. The value in the middle of the list is the median. In this case 6 is the median value.
If two variables, X and Y, have a very strong linear relationship, then A. there is evidence that x causes a change in y B. there is evidence that y causes a change in x C. there might not be any causal relationship between x and y D. None of these alternatives is correct.
C
What is the degree to which sample statistics differ from the equivalent population parameter known as? A. Selection error. B. Sampling error. C. Sample bias. D. Selection bias.
B
Which of the following best describes a relationship that is stochastic? a. influenced by some external "noise" b. described completely within the model c. extremely unlikely to occur in the real world d. simpler than a deterministic model
A stochastic relationship is one in which one value of X may be associated with several different values of Y for different data points. In short, there is an underlying linear relationship, but y is subject to some external "noise" that is causing the additional variation. B. is regarding a deterministic model. C. is false as most relationships will be stochastic in the real world. D. is false as stochastic model is a deterministic model with added "noise".
A fitted least squares regression line ________. a. May be used to predict a value of y if the corresponding X value is given b. Is evidence for a cause-effect relationship between X and Y c. Can only be computed if a strong linear relationship exists between x and y d. None of the above
A
A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, H0: μ≥ 6 and HA:μ < 6, μ stand for ________. a. the mean delivery time b. the standard deviation of the delivery time c. the number of deliveries that took less than 6 hours d. the proportion of deliveries that took less than 6 hours
A
Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. Which of the following hypothesis tests should be performed? a. Left-tailed b. Right-tailed c. Two-tailed d. There is not enough information to answer.
A
If the chosen significance level is α = 0.05, then ________. a. there is a 5% probability of rejecting a true null hypothesis b. there is a 5% probability of accepting a true null hypothesis c. there is a 5% probability of rejecting a false null hypothesis d. there is a 5% probability of accepting a false null hypothesis
A
If the null hypothesis is rejected at a 1% significance level, then ________. a. the null hypothesis will be rejected at a 5% significance level b. the alternative hypothesis will be rejected at a 5% significance level c. the null hypothesis will not be rejected at a 5% significance level d. the alternative hypothesis will not be rejected at a 5% significance level
A
It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)? a. P(X > 16) is greater than P(X < 16). b. P(X > 16) is smaller than P(X < 16). c. P(X > 16) is the same as P(X < 16). d. No comparison can be made with the given information.
A
Simple linear regression analysis differs from multiple regression analysis in that _______. a. simple linear regression uses only one explanatory variable b. the coefficient of correlation is meaningless in simple linear regression c. goodness-of-fit measures cannot be calculated with simple linear regression d. the coefficient of determination is always higher in simple linear regression
A
The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The value of the test statistic is ________. a. z = -1.429 b. t99 = -1.429 c. z = 1.429 d. t99 = 1.429
A
What does it mean when we say that the tails of the normal curve are asymptotic to the x axis? a. The tails get closer and closer to the x axis but never touch it. b. The tails get closer and closer to the x axis and eventually touch it. c. The tails get closer and closer to the x axis and eventually cross this axis. d. The tails get closer and closer to the x axis and eventually become this axis.
A
What does the Y intercept B0 represent: A. The predicted value of Y when X = 0. B. The estimated change in average Y per unit change in X. C. The predicted value of Y. D. The variation around the line of regression.
A
You perform 2000 significance tests using a significance level 0.10. Under the assumption that all of the null hypotheses for the 2000 significance tests are true, how many of the 2000 significance tests would you expect to be statistically significant? A. 200 B. 1800 C. 2000 D. 0 E. None of the above.
A 2000x.10 = 200
Suppose that vehicle speeds at an interstate location have a normal distribution with a mean equal to 70 mph and standard deviation equal to 8 mph. What is the Z-score for a speed of 64 mph? A. − 0.75 B. +0.75 C. −6 D. +6
A 64-70/8 = -0.75
The variance of a sample or a population cannot be _____. a. negative b. calculated c. zero d. less than 1
A Sample variance is 𝑠=∑(𝑥―μ)^2/𝑛―1 and population σ=∑(𝑥―μ)^2/𝑛―1 since n >1 and the square of any number is positive the variance is always positive or zero. It can't be negative
What does the standard error of the estimate measure? A. The total variation of the Y variable. B. The variation around the regression line. C. The explained variation. D. The variation of the X variable.
B
'Children can learn a second language faster before the age of 7'. Is this statement: A. A non-scientific statement B. A one-tailed hypothesis C. A two-tailed hypothesis D. A null hypothesis
B
A sample regression equation is given by: Y=5+0.2𝑥 Suppose that when x = 10, y is observed to be 9. What is the residual of the model prediction and does the model under or overpredict the value of y? a. 2, the model overpredicts y b. 2, the model underpredicts y c. -2, the model overpredicts y d. -2, the model underpredicts y
B
An economist uses regression analysis to determine the relationship between used car price (y) and the age of a car (x). The analysis resulted in the following equation: Y=30,000―500𝑥 The above equation implies that an increase of: a. 1 year in the age of the car is associated with an increase of $500 in the price of the car b. 1 year in the age of the car is associated with a decrease in $500 in the price of the car c. $500 in the price of the car is associated with an increase of 5 years in the age of the car d. 5 years in the age of the car is associated with a decrease of $100 in the price of the car
B
An economist uses regression analysis to determine the relationship between used car price (y) and the age of a car (x). The analysis resulted in the following equation: Y=30,000―500𝑥 The above equation implies that an increase of: a. 1 year in the age of the car is associated with an increase of $500 in the price of the car b. 1 year in the age of the car is associated with a decrease in $500 in the price of the car c. $500 in the price of the car is associated with an increase of 5 years in the age of the car d. 5 years in the age of the car is associated with a decrease of $100 in the price of the car
B
Decide whether the variable is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic A) discrete B) continuous
B
Decide whether the variable is discrete or continuous. Thee height of a player on a basketball team. A) discrete B) continuous
B
Given the least-squares regression line Yhat = 5 - 2X, what may be said about the relationship between the two variables, X and Y? A. The relationship between x and y is positive. B. The relationship between x and y is negative. C. As X increases, so does Y. D. The mean of the independent variable for all levels of the independent variable can be connected by a straight line.
B
Mr. Rumpole believes that the mean income of lawyers is now more than $65 thousand per year. Which is the correct set of hypotheses to test this belief? A. H0: μ ≥ 65 000; HA: μ < 65 000 B. H0: μ ≤ 65 000; HA: μ > 65 000 C. H0: μ = 65 000; HA: μ ≠ 65 000 D. H0: μ < 65 000; HA: μ ≥ 65 000
B
What does the estimated intercept (b0) in regression analysis? a. The slope of the regression line b. The value of the response variable when all of the explanatory variables are 0 c. The relationship between the response and explanatory variables d. The difference in observed and predicted values of the response variable
B
A standard normal distribution is a normal distribution with _____. a. a mean of 1 and a standard deviation of 0 b. a mean of 0 and a standard deviation of 1 c. any mean and a standard deviation of 1 d. any mean and any standard deviation
B Formula for 𝑍=𝑥―μ/𝜎 The numerator demeans the normal distribution so that the mean is equal to zero. While the denominator weighs each observation relative to the standard deviation. Doing so will make the standard deviation 1.
The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is _____. a. H0: μ < 5 Ha: μ≤ 5 b. H0: μ≤ 5 Ha: μ > 5 c. H0: μ > 5 Ha: μ≤ 5 d. H0: μ≥ 5 Ha: μ < 5
B Here we want to prove if the bonus plan increased average sales (μ > 5). We always place what we want to prove in the alternative hypothesis (Ha: μ > 5).
Assume the variance is known, for a one-tailed test (upper tail), the null hypothesis will be rejected at the 0.05 level of significance if the test statistic is _____. a. less than or equal to -1.645 b. greater than 1.645 c. less than 1.645 d. less than -1.96
B Our level of significance is 0.05. We need to find the z score for this level of significance. To do this we need to find the z value in the z table that corresponds to probability of 95% (because we are doing an upper one tailed test). This value is Z = 1.645. To reject the null hypothesis our test statistic has to be greater than 1.645
If the coefficient of determination is a positive value, then the regression equation A. must have a positive slope B. must have a negative slope C. could have either a positive or a negative slope D. must have a positive y intercept
C
A portfolio's annual total returns (in percent) for a five-year period are: -7.14 1.62 2.50 -2.50 9.27 The median and the standard deviation for this sample are the closest to ________. a. 0.75 and 5.46 b. 1.62 and 5.46 c. 1.62 and 6.11 d. 0.75 and 6.11
C
A result is called "statistically significant" whenever A. The null hypothesis is true. B. The alternative hypothesis is true. C. The p-value is less or equal to the significance level. D. The p-value is larger than the significance level.
C
Consider the following simple linear regression model: y = β0 + β1x +ε. The random error term is ________. a. y b. x c. ε d.β0
C
For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ - 2σ, μ + 2σ] is the closest to ________. a. 68% b. 68.26% c. 95% d. 99.73%
C
If X has a normal distribution with μ = 100 and σ = 5, then the probability P(85 ≤X≤ 90) can be expressed in terms of a standard normal variable Z as ________. a.P (2 ≤Z≤ 3) b.P (-3 ≤Z≤ 2) c.P (-3 ≤Z≤ -2) d.P (-3 ≤Z≤ 3)
C
In the last mayoral election in a large city, 47% of the adults over the age of 65 voted Republican. A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed. Let p represent the proportion of the population of all adults over the age of 65 in the city that plan to vote Republican in the next mayoral election. In terms of p, the researcher should test which of the following null and alternative hypotheses? A. H0: p = 0.47 vs. HA: p < 0.47 B. H0: p = 0.47 vs. HA: p > 0.47 C. H0: p = 0.47 vs. HA: p ≠0.47 D. H0 : p > 0.47 vs. HA: p <0.47
C
The average plane flies at 900 km/hour, the speed are normally distributed with a standard deviation of 60 km/hour. What is the probability that a plane picked at random is traveling at a speed less than 810 km/hour? a. 0.1336 b. 0.9332 c. 0.0668 d. 0.0334
C
The following scatterplot indicates that the relationship between the two variables x and y is ________. . : . : . a. Weak and positive b. Strong and positive c. Strong and negative d. No relationship
C
Which of the following statements is true? A. The smaller the population size, the smaller the relationship will be between the sample mean and the population mean. B. The larger the population size, the closer the population mean will be to the sample mean. C. The larger the sample size, the closer the sample mean will be to the population mean. D. The smaller the sample size, the closer the sample mean will be to the population mean.
C
A regression model that incorporates three independent variables to explain the variation in one dependent variable is called ____. a. simple b. strong c. complex d. weak
C A model with more than one independent variable is known as a COMPLEX model. A model with only one independent variable is known as simple.
Which of the following relationships might you expect to be negative? a. a person's age and number of known words b. cups of coffee consumed and energy level c. liters of pesticide sprayed and number of insects on crops d. level of education and wage
C As pesticides kill insects the more you spray the less insects you expect to be alive so we have a negative relationship between the amount of pesticides sprayed and the number of insects on crops.
If X has a normal distribution with μ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as ________. a. P (2 ≤ Z ≤ 1) b. P (-2 ≤ Z ≤ 1) c. P (-2 ≤ Z ≤ -1) d. P (-2 ≤ Z ≤ -2)
C Find the z value of x = 90 and x = 95. For x = 90: Z = (90 - 100)/5 = -2. For x = 95: Z = (95 - 100)/5 = - 1. Therefore P (90 < x < 95) = P (-2 < z < -1).
In the Standard Normal Distribution, which of the following is equivalent to the probability that Z < -2? a. Prob(Z > -2) b. Prob Z < 2) c. Prob(Z > 2) d. Prob (Z = 2)
C From the z table P (Z < -2) = 0.0228. Returning to the Z table P (Z > 2) = 0.0228. The answer is C. Another way to answering this question: A standard normal distribution is symmetric, this means that prob (Z < -x) will be the same as prob (Z > x) for any x in the distribution.
Which of the following meets the requirements of a cluster sample? a. A population can be divided into 50 city blocks. The sample will include one hundred people who volunteer for the sample from any city block. b. A population can be divided into 50 city blocks. The sample will include one hundred people chosen at random, without regard to the city block where they live. c. A population can be divided into 50 city blocks. The sample will include all residents from two randomly chosen city blocks. d. A population can be divided into 50 city blocks. The sample will include two people chosen at random from each city block.
C In a cluster sample we separate the population into groups and randomly select entire groups to sample. In this case we separated the population in 50 city blocks and randomly chose two city blocks
In an attempt to predict the outcome of a local election, a student travels around the UK campus and only asks political science students who they would vote for. What type of bias will this survey likely have? a. non-response bias b. type II bias c. selection bias d. pattern bias
C The bias here comes on how we SELECTED the sample. The sample is not a random selection of the UK student body. So we have C. selection bias.
The median of a sample will always equal the _____. a. mode b. mean c. 50th percentile d. All of the answers are correct.
C The median is the middle value of a sample arranged in ascending order. So 50% of sample will be below it and 50% will be above it. Thus D. it will be the 50th percentile. B. is not correct. The mean and median will be same ONLY if we have a normal distribution.
The measure of variation that is influenced most by extreme values is the _____. a. variance b. standard deviation c. range d. median
C The range is the difference between the highest number and the lowest number. Since an extreme value will change either or both the highest or lowest number it will have a direct impact on the range. It will affect the variance and standard deviation but at a smaller degree, especially in samples with large n. If we replace the highest value in a sample with an extremely high value, it will not affect the median as it is still the same value in the middle of the sample.
The sample variance _____. a. is always smaller than the true value of the population variance b. is always larger than the true value of the population variance c. could be smaller, equal to, or larger than the true value of the population variance d. can never be zero
C The sample variance can be smaller, equal to or larger than the true variance as it depends on the sample chosen and the size of the sample.
The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is _____. a. H0: p < .30 Ha: p≥ .30 b. H0: p≤ .30 Ha: p > .30 c. H0: p≥ .30 Ha: p < .30 d. H0: p > .30 Ha: p≤ .30
C We always want to have what we want to prove in our alternative hypothesis. Since the newspaper claims (p ≥ 0.30) we want to test whether the proportion is less than 30%. So our alternative hypothesis is Ha: p < 0.30. Another way to answer this question is that the newspaper claims AT LEAST 30% of students are majoring in business. The null hypothesis should always have the equal sign so our null is H0: p≥ 0.30
In the simple linear regression equation, the symbol X represents the A. estimated or predicted response B. estimated intercept C. estimated slope D. explanatory variable
D
A hypothesis test is done in which the alternative hypothesis (HA) is that more than 10% of a population is left-handed. The p-value for the test is calculated to be 0.25. Which statement is correct? Assume that α = 0.05. A. We can conclude that more than 10% of the population is left-handed. B. We can conclude that more than 25% of the population is left-handed. C. We can conclude that exactly 25% of the population is left-handed. D. We cannot conclude that more than 10% of the population is left-handed.
D
A radar unit is used to measure speeds of cars on a highway. The speeds are normally distributed with a mean of 70 mph and a standard deviation of 5 mph. What is the probability that a car picked at random is traveling at more than 80 mph? a. 0.95 b. 0.975 c. 0.05 d. 0.025
D
For data to be normally distributed, which of the following characteristics should it have? A. To be defined as 'normal' a distribution should be symmetrical about the mean, it should meet the x axis at infinity and it should be leptokurtic. B. To be defined as 'normal' a distribution should be symmetrical about the mean, it should meet the x axis at infinity and it should be platykurtic. C. To be defined as 'normal' a distribution should be symmetrical about the mean, it should meet the x axis at infinity and it should be positively skewed. D. To be defined as 'normal' a distribution should be symmetrical about the mean, it should meet the X axis at infinity and it should be bell shaped.
D
In a hypothesis test: A. the null hypothesis is the researcher's hypothesis B. the alternate hypothesis is always assumed to be true C. the alternate hypothesis is accepted unless there is sufficient evidence to say otherwise D. the null hypothesis is not rejected unless there is sufficient evidence to reject it.
D
In general, the null and alternative hypotheses are ________. a. additive b. correlated c. multiplicative d. mutually exclusive
D
In the sample regression equation yhat = b0 + b1x, What is yhat? a. The y-intercept b. The slope of the equation c. The value of y when x = 0 d. The predicted value of y, given a specific x value
D
Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim. a. H0: p = 0.84 and HA: p ≠ 0.84 b. H0: p < 0.84 and HA: p ≥ 0.84 c. H0: p ≤ 0.84 and HA: p > 0.84 d. H0: p ≥ 0.84 and HA: p < 0.84
D
The Boom Company has recently decided to raise the salaries of all employees by 10%. Which of the following is (are) expected to be affected by this raise? a.Mean and mode only b.Mean and median only c.Mode and median only d.Mean, median, and mode
D
The mean of a standard normal probability distribution _____. a. is always equal to 1 b. can be any value as long as it is positive c. can be any value d. None of the answers is correct.
D
The value of the _______ is used to estimate the value of the population parameter. a. population statistic b. sample parameter c. population estimate d. sample statistic
D
Which of the following can NOT be answered from a regression equation? A. Predict the value of Y at a particular value of X. B. Estimate the slope between Y and X. C. Estimate whether the linear association is positive or negative. D. Estimate whether the association is linear or non-linear
D
Which of the following does not represent a continuous random variable? a. Heights and weights of newborn babies. b. Time to do grocery shopping c. Driving time between Chicago and New York d. Number of students in the classroom
D
Which of the following represents an appropriate set of a population hypotheses? a. H0: Xbar = 0, HA: Xbar ≠ 0 b. H0: Xbar < 0, HA: Xbar > 0 c. H0: μ < 0, HA: μ > 0 d. H0: μ = 0, HA: μ≠ 0
D
Which of the following statements about variance is the most accurate? a.Variance is the square root of the standard deviation. b.Variance can be either positive or negative. c.Variance is denominated in the same units as the original data. d.Variance is the average of the squared deviations from the mean.
D
All of the following are discrete variables except: a. result of a coin flip b. outcome of a die roll c. choosing a random color from a list d. a person's height
D A discrete variable is a variable that has a countable number of distinct values. A. has two distinct values (head, tails). B. has 6 countable values (1, 2, 3, 4, 5, and 6). C has list of colors (red, blue, etc.). D. a person's height is infinitely uncountable within an interval, so it is NOT discrete.
The mean of a standard normal probability distribution _____. a. is always equal to 1 b. can be any value as long as it is positive c. can be any value d. None of the answers is correct.
D A standard normal probability distribution is a normal distribution standardized so that the mean is equal to zero (μ (mu) = 0) and variance equal to one (σ (sigma) = 1).
In regression analysis, if the dependent variable is measured in dollars, the independent variable ____. a. must also be measured in dollars b. can be measured in any unit of currency c. cannot be measured in dollars d. can be measure in any units
D Can be measured, in dollars, in pounds, in Yards, as a percentage, anything, any unit. b. is correct but incomplete.
Suppose a sample regression equation is given by 𝑦 = 3 + 0.40x. Suppose when x is 10, y is observed to be 8. What is the residual of the model prediction and does the model under or overpredicts the value of y? a. = −1, the model overpredicts y b. = −1, the model underpredicts y c. = 1, the model overpredicts y d. = 1, the model underpredicts y
D Find the predicted value of y when x = 10. Y = 3 + 0.40 (10) = 7. The predicted value is 7 and the actual value is 8. So we underpredict 7 by 1
Why do researchers use sample statistics instead of population parameters? a. It is expensive to gather data on entire population b. It is time consuming to gather data on entire population c. Sample statistics are more accurate than population parameters d. Both a and b
D Gathering data is very expensive financially (a) and very expensive in terms of time spent (b). C is incorrect as the population parameter is the TRUE parameter.
Which of the following has the highest value (Standard Normal Distribution)? a. Prob (Z < 0) b. Prob (Z > 0) c. Prob (Z > 1) d. Prob (Z < 1)
D Go to the z table: P (Z < 0) = 50, P (Z > 0) = 50, P (Z > 1) = 0.1587, P (Z < 1) = 0.8413. The largest number is d. Prob (Z < 1).
A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: yhat = 50,000 − 8x The above equation implies that an increase of _____. a. $1 in price is associated with a decrease of $8 in sales b. $8 in price is associated with an increase of $8,000 in sales c. $1 in price is associated with a decrease of $42,000 in sales d. $1 in price is associated with a decrease of $8,000 in sales
D If we increase x by 1 y will decrease by 8 (definition of B1 coefficient). Note that y is in thousands. So, a decrease in 8 signifies a decrease of $8,000. Thus D. is the answer: a $1 in price increase decreases sales by $8,000.
If a hypothesis is rejected at the 5% level of significance, it _____. a. will always be rejected at the 1% level b. will always be accepted at the 1% level c. will never be tested at the 1% level d. may or may not be rejected at the 1% level
D If we reject a hypothesis at the 5% level, it depends on the claim if we reject the hypothesis at the 1% level. As an example, assume a mean = 10. Also assume the CI at 5% significance is (5, 10) and the CI at 10% significance is (0, 15). The value 12 will be rejected at 5% but not at 10%. While a value of 20 will be rejected at both.
As a general guideline, the research hypothesis should be stated as the: a. tentative assumption b. disproven hypothesis c. null hypothesis d. alternative hypothesis
D We always want to state what we want to prove (our research hypothesis) as the alternative hypothesis.
A meteorologist stated that the average temperature during July in Chattanooga was 76 degrees. A colleague says that might not be true. A sample of July temperatures over a 32-year period was taken. The correct set of hypotheses is _____. a. H0: μ < 76; Ha: μ≤ 76 b. H0: μ≤ 76; Ha: μ > 76 c. H0: μ≠ 76; Ha: μ = 76 d. H0: μ = 76; Ha: μ≠ 76
D We want to prove that the average temperature was NOT 76. What we want to prove goes in the alternative hypothesis. Thus Ha: u ≠76
An investment manager states that the average yearly rate of return on the stocks she recommends is at least 15.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____. a. H0: μ < 15.0%; Ha: μ≥ 15.0% b. H0: μ≤ 15.0%; Ha: μ > 15.0% c. H0: μ > 15.0%; Ha: μ≤ 15.0% d. H0: μ≥ 15.0%; Ha: μ < 15.0%
D We want to prove that the stocks of return are less than 15% so our alternative hypothesis will be Ha: μ < 15.0% (d). Similar to question 24.
According the empirical rule for normally distributed variables, 75% of the values fall within one standard deviation of the mean.
FALSE
Another name for an explanatory variable is the dependent variable.
FALSE
Null hypothesis should contain the statement you are hoping to prove.
FALSE The alternative hypothesis should be what contains the statement you are trying to prove not the null hypothesis. Such as if the mean is less than, greater than, or not equal to.
When performing regression analysis, a higher level of variance typically indicates a more accurate model.
FALSE The higher the variance, the more spread out the observations will be around the estimated regression line. This will lead to a higher degree of uncertainty.
The variance and standard deviation are the most widely used measures of central location.
FALSE Variance and standard deviation are the most widely used measures of dispersion, or how spread out the observations will be. Mean and median are used to measure central location.
Stratified sampling is generally more accurate than cluster sampling.
TRUE With a cluster sampling you might randomly pick groups that are not representative of the population. For example, we want to understand the behavior of the UK student population. If we cluster by major and we randomly choose two majors, economics and finance, these groups may not be representative of the whole UK student body. While with stratified sampling, where we get a random sample of each major, our sample will be a better representation of the UK student body.
