BSTATS Final Exam

The probability that a normal random variable is less than its mean is ______.

0.5

Which of the following relationships can be concluded from examining the correlation coefficient?

-A positive relationship -A negative relationship -No relationship

Which of the following is true of the standard error of the estimate?

-Theoretically, its value has no predefined upper limit. -It is based on the squared deviations between the actual and predicted values of the response variable. -It is a measure of the accuracy of the regression model.

What is the Benoulli process?

A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are only two possible outcomes (success and failure), and in each trial the probability of a success (and failure) remains the same.

What is another name for an explanatory variable?

An explanatory variable is sometimes called the independent variable, predictor variable, control variable, or regressor.

What makes an R2 value stronger?

Assuming that two regression models have the same number of explanatory variables, the one with greater R2 value is stronger.

The accompanying chart shows the numbers of books written by each author in a collection of cookbooks. What type of chart is this?

Bar chart for qualitative data

What makes an event mutually exclusive?

Events are mutually exclusive if they do not share any common outcome of a random experiment. Events are exhaustive if all possible outcomes of a random experiment are included in the event.

What is the name of the variable that is used to predict another variable?

Explanatory

A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

False

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

False

A parameter is a random variable, whereas a sample statistic is a constant.

False

A pie chart is a segmented circle that portrays the categories and relative sizes of some quantitative variable.

False

A residual is the difference between the predicted and observed values of y.

False

Another name for an explanatory variable is the dependent variable.

False

For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level 100(1-a)%.

False

For an experiment in which a single die is rolled, the sample space may be {1, 1, 2, 3, 4, 5}.

False

For any population X with expected value µ and standard deviation σ, the sampling distribution of will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n < 30.

False

Given that the probability distribution is normal, it is completely described by its mean μ > 0 and its standard deviation σ > 0.

False

If two linear regression models have the same number of explanatory variables, a model with an R2 value of 0.45 is a better prediction model than a model with an R2 value of 0.65.

False

In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes randomly selected observations from each cluster, which are proportional to the cluster's size.

False

Like the z distribution, the tdf distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.

False

Scatterplot is a graphical tool that is focused on describing one variable.

False

Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.

False

The addition rule is used to determine the probability of the union of two events occurring and is defined as a sum of the probabilities of both events.

False

The central limit theorem approximation improves as the sample size decreases.

False

The probability of a union of events can be greater than 1.

False

We use a population parameter to make inferences about a sample statistic.

False

What is the width for a confidence interval?

For a given sample size n and population standard deviation σ, the width of the interval is wider, the greater the confidence level .

What happens in a cluster random sampling?

In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes observations from randomly selected clusters. Instead of taking a subset from each cluster, the entire cluster is selected as part of the sample.

Which of the following is not true of the standard error of the estimate?

It can take on negative values

A Type I error is committed when we reject the null hypothesis, which is actually true.

True

A bar chart may be displayed horizontally.

True

A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean

True

Bias refers to the tendency of a sample statistic to systematically over-or underestimate a population parameter.

True

Consider these events. A = The survey respondent is less than 40 years old. B = The survey respondent is 40 years or older. Events A and B are mutually exclusive and exhaustive.

True

For a given confidence level and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size n.

True

For a given sample size n and population standard deviation σ, the width of the interval is wider, the greater the confidence level .

True

For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.

True

For any population X with expected value µ and standard deviation σ, the sampling distribution of will be approximately normal if the sample size n is sufficiently large. As a general guideline, the normal distribution approximation is justified when n ≥ 30.

True

In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum, which are proportional to the stratum's size.

True

The method of least squares picks the slope and intercept of the sample regression equation by minimizing SSE.

True

The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.

True

The standard normal table is also referred to as the z table.

True

The variance is an average squared deviation from the mean.

True

Two events A and B are independent if the probability of one does not influence the probability of the other.

True

When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.

True

Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown. How are these two cases treated differently?

Use the z table when σ is known; use the t table when σ is unknown.

What do we use sample statistic for?

We use a sample statistic, or simply statistic, to make inferences about an unknown population parameter.

A 99% confidence interval estimate can be interpreted to mean that

if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. !!ALSO!! we have 99% confidence that we have selected a sample whose interval does include the population mean.

The central limit theorem approximation improves as the sample size____________.

increases

If event A and event B cannot occur at the same time, then events A and B are said to be

mutually exclusive.

In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a ______ interval.

narrower

When we reject the null hypothesis when it is actually false, we have committed _________.

no error

If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α = 0.05, then the correct conclusion is to ____________________.

not reject the null hypothesis

A ________ is a numerical quantity not computed from the data of a sample and is the size of the critical region used in reaching a decision on whether or not to reject the null hypothesis.

significance level

Consider the following simple linear regression model: y = β0 + β1x + ε. β0 and β1 are ________.

the unknown parameters

The width of the confidence interval is _____ times the margin of error.

two

Consider the following simple linear regression model: y = β0 + β1x + ε. The explanatory variable is ________.

x

Consider the following simple linear regression model: y = β0 + β1x + ε. The random error term is ________.

ε

In a simple linear regression model, if the points on a scatter diagram lie on a straight line with a negative slope, which of the following is the coefficient of determination?

+1

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the standard error of the estimate?

0

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 ______.

95%

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?

A larger sample size reduces the margin of error.

What is a normal distribution characterized by?

A normal distribution is completely characterized by its mean and standard deviation, but while the standard deviation is always positive, the mean of the normally distributed random variables can be positive or negative.

What is a parameter?

A parameter is a constant, although its value may be unknown. A sample statistic, such as the sample mean or the sample proportion, is a random variable whose value depends on the chosen random sample.

What is a pie chart?

A pie chart is a segmented circle whose segments portray the relative (or percent) frequencies of the categories of some qualitative variable.

What is a residual?

A residual is the difference between the observed and predicted values of y.

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event Ac and what is the probability of this event?

Ac = {TTT, HHT, HTH, THH, HHH}; P(Ac) = 0.625

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

Do not reject Ho; we cannot conclude that the mean differs from zero.

The accompanying chart shows the number of books written by each author in a collection of cookbooks. What type of data is being represented?

Qualitative, nominal

What is the sample space for when a single die is rolled?

Sample space for a six-sided die always consists of numbers 1 through 6.

What is selection bias?

Selection bias refers to a systematic exclusion of certain groups from consideration for the sample.

What is the addition rule?

The addition rule is calculated as P(A U B) = P(A) + P(B) − P(A n B). It is the sum of the probabilities minus any intersection between the two events.

If, as a result of a hypothesis test, we do not reject the null hypothesis when it is false, then we have committed

a Type II error.

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

a two-tail test for is used.

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. To determine whether there has been a decrease in the average number of customers visiting the dealership daily, At the 5% significance level, the decision is to ___________.

do not reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800

Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.38. If we choose a 5% significance level, then we ___________________________________________.

do not reject the null hypothesis and conclude that the population mean is not significantly different from zero

Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) ______.

estimate

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________.

reject the null hypothesis

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

test statistic

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________.

the franchiser builds on an unacceptable site

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ___________________________.

the mean GPA of the university honors students

If the null hypothesis is rejected at a 1% significance level, then _____________.

the null hypothesis will be rejected at a 5% significance level