Quant Analysis Final Exam

In a random sample of 400 registered voters, 120 indicated they plan to vote for Trump for President. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Trump.

(0.25, 0.34)

The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion σp̄?

. 0.039

The t value for a 99% confidence interval estimation based upon a sample of size 10 is _____

. 3.249

A normally distributed error term with a mean of zero would _____.

allow more accurate modeling

In a linear regression model, the variable (or variables) used for predicting or explaining values of the response variable are known as the _____. It(they) is(are) denoted by x.

independent variable

Regression analysis involving one dependent variable and more than one independent variable is known as _____.

multiple regression

In a simple linear regression model, y = ß0 + ß1x + ε the parameter ß1 represents the _____.

slope of the true regression line

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as _____

statistical inference

When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is _____.

zero

The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the point estimate of the proportion of the population that logged onto Facebook that day?

. 0.35

The _____ function is used to generate a pseudorandom number in Excel.

. RAND()

The Excel function _____ generates integer values between lower and upper bounds.

. RANDBETWEEN

___ is the process of determining that a simulation model provides an accurate representation of a real system.

. Validation

The range of computer-generated random numbers is ____

. [0, 1)

A variable used to model the effect of categorical independent variables in a regression model is known as a _____.

. dummy variable

The coefficient of determination _____

. is used to evaluate the goodness of fit

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size ____

. n has the same probability of being selected

The scatter chart below displays the residuals versus the dependent variable, t. Which of the following conclusions can be drawn based upon this scatter chart?

. residuals are not independent.

A _____ is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.

. scatter chart

In the graph of the simple linear regression equation, the parameter ß1 is the _____ of the true regression line.

. slope

In a simple linear regression analysis the quantity that gives the amount by which the dependent variable changes for a unit change in the independent variable is called the _____.

. slope of the regression line

The least squares regression line minimizes the sum of the ____

. squared differences between actual and predicted y values

he graph of the simple linear regression equation is a(n) ___

. straight line

The _____ is a measure of the error that results from using the estimated regression equation to predict the values of the dependent variable in the sample.

. sum of squares due to error (SSE)

The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. Compute the 95% confidence interval for the population proportion.

0.35+-1.96

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03

0.43

What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89?

18.43

Which statement is NOT true?

Rejecting the null hypothesis when it is true is a Type II error.

Larger values of α have the disadvantage of increasing the probability of making a _____.

Type I error

The time it takes to manufacture a product is modeled by a continuous distribution. The time to manufacture one unit can take anywhere from 5 to 6 minutes with equal probability. What distribution can be used to model the random variable, production time?

Uniform distribution

_____ refers to the data set used to compare model forecasts and ultimately pick a model for predicting values of the dependent variable.

Validation set

A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time μ = 45 hours. The production manager has developed a new procedure for producing the part. He believes that the new procedure will decrease the population mean amount of time required to produce the part. After training a group of production line workers, a random sample of 25 parts will be selected and the average amount of time required to produce the parts will be determined. If the switch is made to the new procedure, the cost to implement the new procedure will be more than offset by the savings in manpower required to produce the parts. Use the hypotheses: Ho: μ ≥ 45 hours and Ha: μ < 45 hours. Determine the p value of the test statistic if the sample mean amount of time is = 43.118 hours with the sample standard deviation s = 5.5 hours.

. 0.04999

Prediction of the mean value of the dependent variable y for values of the independent variables x1, x2, . . . , xq that are outside the experimental range is called _____.

extrapolation

Prediction of the value of the dependent variable outside the experimental region is called _____

extrapolation

The finite correction factor should be used in the computation of the standard deviation of the sample mean and the standard population when n / N is _____.

greater than 0.05

The choice of the probability distribution for a random variable can be guided by _____.

historical data

A distribution of a random variable for which values extremely larger or smaller than the mean are increasingly unlikely can possibly be modeled as a(n) _____ probability distribution

normal

The type of distribution shown in the graph below is a(n) _____ distribution.

normal

Fitting a model too closely to sample data, resulting in a model that does not accurately reflect the population is termed as _____

overfitting

The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as _____.

risk analysis

The value of the _____ is used to estimate the value of the population parameter.

sample statistic

A regression analysis involving one independent variable and one dependent variable is referred to as a _____

simple linear regression

The basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population mean is _____.

the central limit theorem

In a base-case scenario, the output is determined by assuming

the most likely values for the random variables of a model

All the values of computer-generated random numbers are ___

uniformly distributed

The profit realized by the sales of a particular item follows a normal distribution with a mean of $0.5 million per quarter and a standard deviation of $0.1 million per quarter. What percent of the quarters can be expected to see a profit of at least $0.5 million?

. 50%

_____ refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter.

. Interval estimation

Which of the following regression models is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable in the model?

. Quadratic regression model

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. The 95% confidence interval for the true mean number of pushups that can be done is _____

8.56 to 21.40

_____ is used to test the hypothesis that the values of the regression parameters ß1, ß2, ... ßq are all zero.

An F test

The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are _____

B0 and B1

Which of the following is a disadvantage of using simulation?

Each simulation run provides only a sample of how the real system will operate.

In reviewing the graph below, which of the following inferences can be drawn about the monthly salary?

The average monthly salary is $3,000.

Which of the following cannot be described by a discrete probability distribution?

The cost of parts for manufacturing an item, where the parts can take on any value between $80 and $100.

The scatter chart below displays the residuals versus the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart?

The model fails to capture the relationship between the variables accurately.

Which of the following inferences about a variable of interest can be drawn from the graph given below?

The variable is equally likely to take any value between 20 and 40.

____ is the data set used to build the candidate models.

Training set

The proportion of dental procedures that are extractions is 0.16. Which of the following exemplifies a Type I error in this situation?

We reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually 0.16.

A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called _____

a dummy variable

A Type I error is committed when _____

a true null hypothesis is rejected

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. What is the standard error of the mean?

a. 2.876

Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed: H0: μ = 11, Ha: μ > 11.

a. Right-tailed

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.

a. approximately normal for large sample sizes

A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time μ = 45 hours. The production manager has developed a new procedure for producing the part. He believes that the new procedure will decrease the population mean amount of time required to produce the part. After training a group of production line workers, a random sample of 25 parts will be selected and the average amount of time required to produce them will be determined. If the switch is made to the new procedure, the cost to implement the new procedure will be more than offset by the savings in manpower required to produce the parts. Use the hypotheses: H0: μ ≥ 45 hours and Ha: μ < 45 hours. If the sample mean amount of time is = 43.118 hours with the sample standard deviation s = 5.5 hours, give the appropriate conclusion, for α = 0.025.

b. Do not reject H0, do not switch to the new procedure.

One reason a sample may fail to represent the population of interest is _____.

sampling error

A sample of 37 AA batteries had a mean lifetime of 584 hours. A 95% confidence interval for the population mean was 579.2 < μ < 588.8. Which statement is the correct interpretation of the results

b. We are 95% confident that the mean lifetime of all the bulbs in the population is between 579.2 hours and 588.8 hours.

In a _____ distribution, a random variable can take any value in a specified rang

b. continuous probability

If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to _____.

be an unbiased estimator of the population parameter

In interval estimation, as the sample size becomes larger, the interval estimate _____

becomes narrower

As the number of degrees of freedom for a t distribution inceases, the difference between the t distribution and the standard normal distribution _____.

becomes smaller

Using an α = 0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion _____.

becomes wider

What are the two decisions that you can make from performing a hypothesis test?

c. Reject the null hypothesis; Fail to reject the null hypothesis

The scatter chart below displays the residuals versus the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart?

c. The residual distribution is not normally distributed.

The outcome of a simulation experiment is a(n)

c. probability distribution for one or more output measures

In simulation analysis, the _____ of random variables can be adjusted to determine the impact of the assumptions about the shape of the uncertainty on the results

c. probability distributions

procedure for using sample data to find the estimated regression equation is _____

c. the least squares method

A pizza shop advertises that they deliver in 30 minutes or less or it is free. People who live in homes that are located on the opposite side of town believe it will take the pizza shop longer than 30 minutes to make and deliver the pizza. A random sample of 50 deliveries to homes across town was taken and the mean time was computed to be 32 minutes. What is the appropriate symbol to represent the value, 32?

c. x= 32

The _____ is a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.

coefficient of determination

The _____ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.

confidence level

An input to a simulation model that is selected by the decision maker is known as a ______

controllable input

Assessing the regression model on data other than the sample data that was used to generate the model is known as ____

cross-validation

For a given mean and standard deviation, the _____ function in Excel is used to generate a value for the random variable characterized by a normal distribution.

d. NORM.INV

The values for random variables in a Monte Carlo simulation are ______.

d. generated randomly from probability distributions

The process of making a conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as _____.

d. hypothesis testing

A one-tailed test is a hypothesis test in which the rejection region is

d. in one tail of the sampling distribution

A parameter is a numerical measure from a population, such as

d. μ

In a linear regression model, the variable that is being predicted or explained is known as _____. It is denoted by y and is often referred to as the response variable

dependent variable

The random variables corresponding to the interarrival times of customers and the service times of the servers are commonly part of a(n) _____ simulation

discrete-event

In the simple linear regression model, the _____ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between the variables.

error term

The _____ is the range of values of the independent variables in the data used to estimate the regression model.

experimental region

In Excel, the expression LN(RAND())*(-m) would generate a(n) _____ random variable with mean m.

exponential

The prespecified value of the independent variable at which its relationship with the dependent variable changes in a piecewise linear regression model is referred to as the ____

knot

Which of the following numbers cannot result from the Excel function =NORM.INV(RAND( ), 100, 10)?

ll of these numbers can result from this Excel function.

Two approaches to drawing a conclusion in a hypothesis test are _____.

p-value and critical value

A simple random sample of 31 observations was taken from a large population. The sample mean equals 5. Five is a ____

point estimate

The population parameter value and the point estimate differ because a sample is not a census of the entire population, but it is being used to develop the ____

point estimate

The purpose of statistical inference is to make estimates or draw conclusions about a _____.

population based upon information obtained from the sample

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same _____ and each element is selected _____

population; independently

A disadvantage of the simple what-if analyses is that ____

there is no indication of the likelihood of various output values

A set of values for the random variables is called a(n) ____

trial

When the expected value of the point estimator is equal to the population parameter it estimates, it is said to be ____

unbiased

The random numbers generated using Excel's RAND function follows a _____ probability distribution between 0 and 1.

uniform

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. If we would like to capture the population mean with 95% confidence the margin of error would be _____.

2.262(9/10)

In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is _____.

23

The weekly demand for an item in a retail store follows a uniform distribution over the range 70 to 83. What would be the weekly demand if its corresponding computer-generated value is 0.5?

76.5

The _____ function in Excel is used to compute the statistics required to create a histogram.

FREQUENCY

Which statement is NOT true?

Failing to reject the null hypothesis when it is false is a Type I error.

A student wants to determine if pennies are really fair when flipped, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. If p denotes the true probability of a penny landing heads up when flipped, what are the appropriate null and alternative hypotheses?

H0: p = 0.5, Ha: p ≠ 0.5.

The owners of a fast food restaurant have automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, some variation in this amount. The company does not want the machine to systematically over fill or under fill the cups. Which of the following gives the correct set of hypotheses?

H0: u = 12, Ha: u ≠ 12

A pizza shop advertises that they deliver in 30 minutes or less or it is free. People who live in homes that are located on the opposite side of town believe it will take the pizza shop longer than 30 minutes to make and deliver the pizza. Write the null and alternative hypotheses that can be used to conduct a significance test.

H0: u ≤ 30, Ha: u > 30

The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are _____.

H0: u ≥ 50.1, Ha: u < 50.1

refers to the scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable.

Interaction

_____ refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter.

Interval estimation

Which of the following is true of verification?

It is largely a debugging task.

A _____ uses repeated random sampling to represent uncertainty in a model representing a real system and that computes the values of model outputs.

Monte Carlo simulation

____ refers to the degree of correlation among independent variables in a regression model.

Multicollinearity

Which of the following functions computes a value such that 2.5% of the area under the standard normal distribution lies in the upper tail defined by this value?

NORM.S.INV(0.975)

Which of the following cannot be modeled by a continuous distribution?

Number of products produced in an hour

Which of the following Excel functions would generate random integers from 0 to 100?

RANDBETWEEN(0, 100)

Which of the following parameters is required to convert a computer-generated random variable into a uniform random variable?

Range of the distribution

_____ is a statistical procedure used to develop an equation showing how two variables are related.

Regression analysis

A null and alternative hypothesis for a one proportion z test are given as H0: p ≥ 0.8, Ha: p < 0.8. This hypothesis test is __

lower-tailed

Statistical significance at the 0.01 level is _____ than significance at the 0.05 level.

more difficult to achieve

You are _____ to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance.

more likely

The degree of correlation among independent variables in a regression model is called _____.

multicollinearity

A description of the range and relative likelihood of possible values of an uncertain variable is known as a ____

probability distribution

A(n) _____ is an input to a simulation model whose value is uncertain and described by a probability distribution.

random variable

A simulation model extends spreadsheet modeling by _____

replacing the use of single values for parameters with a range of possible values

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.

residual

The process of determining that a computer program implements a simulation model as it is intended is known as ____

verification

The processes that generate big data can be described by the following four attributes or dimensions:

volume, variety, veracity, and velocity

A _____ analysis involves considering alternative values for the random variables and computing the resulting value for the output

what-if

In the graph of the simple linear regression equation, the parameter ß0 represents the _____ of the true regression line.

y-intercept