ECO 391 Exam 1

regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: = 50,000 − 8x The above equation implies that an increase of _____.

$1 in price is associated with a decrease of $8,000 in sales

A portfolio's annual total returns (in percent) for a five-year period are: -7.14 1.62 2.50 -2.509.27 The median and the standard deviation for this sample are the closest to ________.

.62 and 6.11

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 travelling at more than 80 mph?

0.025

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 travelling at a speed less than 810 km/hour?

0.0668

The probability P (Z < −1.28) is closest to ________.

0.10

Using the Standard Normal Distribution, find the probability that Z > 1.

0.1587

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:

1 year in the age of the car is associated with a decrease in $500 in the price of the car

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?

2, the model underpredicts y

A researcher has collected the following sample data.

6

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%

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?

= 1, the model underpredicts y

Which of the following meets the requirements of a cluster sample?

A population can be divided into 50 city blocks. The sample will include all residents from two randomly chosen city blocks.

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

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

Which of the following is not a correct way to state an alternative hypothesis?

A. HA: μ = 0

What does the Y intercept B0 represent:

A. The predicted value of Y when X = 0.

If we fail to reject the null hypothesis (H0) that means that the test statistics was not in the rejection region.

A. True

A statistic is:

A. a sample characteristic

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

Parameters and statistics...

B Describe the population and the sample, respectively.

Decide whether the variable is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic

B) continuous

Decide whether the variable is discrete or continuous. Thee height of a player on a basketball team.

B) continuous

Evaluate 𝑃(−1.1≤𝑍≤ 0.21)

B. 0.4475

'Children can learn a second language faster before the age of 7'. Is this statement:

B. A one-tailed hypothesis

What do residuals represent?

B. The difference between the actual Y values and the predicted Y values.

What does the slope (β1) represent?

B. The estimated change in average Y per unit change in X.

given the least-squares regression line Yhat = 5 - 2X, what may be said about the relationship between the two variables, X and Y?

B. The relationship between x and y is negative.

Assuming a linear relationship between X and Y, which of the following is true if the estimated coefficient equals -0.30?

B. The slope (β1) is negative.

What does the standard error of the estimate measure?

B. The variation around the regression line.

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?

C. H0: p = 0.47 vs. HA: p not equal to 0.47

Which of the following statements is true?

C. The larger the sample size, the closer the sample mean will be to the population mean.

A result is called "statistically significant" whenever

C. The p-value is less or equal to the significance level.

If the coefficient of determination is a positive value, then the regression equation

C. could have either a positive or a negative slope

If two variables, X and Y, have a very strong linear relationship, then

C. there might not be any causal relationship between x and y

Which of the following can NOT be answered from a regression equation?

D. Estimate whether the association is linear or non-linear

For data to be normally distributed, which of the following characteristics should it have?

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.

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.

D. We cannot conclude that more than 10% of the population is left-handed.

In the simple linear regression equation, the symbol X represents the

D. explanatory variable

In a hypothesis test:

D. the null hypothesis is not rejected unless there is sufficient evidence to reject it.

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

Explanatory

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

The letter Z is used to denote a random variable with any normal distribution.

False

The null hypothesis should contain the statement you are hoping to prove.

False

The variance and standard deviation are the most widely used measures of central location.

False

When performing regression analysis, a higher level of variance typically indicates a more accurate model.

False

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.

H0: p ≥ 0.84 and HA: p < 0.84

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 _____.

H0: p≥ .30 Ha: p < .30

Which of the following represents an appropriate set of a population hypotheses?

H0: μ = 0, HA: μ≠ 0

Which of the following are two-tailed tests?

H0: μ = 10, HA: μ≠ 10

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 _____.

H0: μ = 76; Ha: μ≠ 76

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 _____.

H0: μ≤ 5 Ha: μ > 5

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 _____.

H0: μ≥ 15.0%; Ha: μ < 15.0%

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?

Left-tailed

A fitted least squares regression line ________.

May be used to predict a value of y if the corresponding X value is given

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?

Mean, median, and mode

The mean of a standard normal probability distribution _____.

NOT any of the following: is always equal to 1, can be any value as long as it is positive, can be any value

Which of the following does not represent a continuous random variable?

Number of students in the classroom

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 ________.

P (-2 ≤ Z ≤ -1)

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 ________.

P (-3 ≤Z≤ -2)

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)?

P(X > 16) is greater than P(X < 16).

Which of the following has the highest value (Standard Normal Distribution)?

Prob (Z < 1)

In the Standard Normal Distribution, which of the following is equivalent to the probability that Z < -2?

Prob(Z > 2)

What is the degree to which sample statistics differ from the equivalent population parameter known as?

Sampling error.

The following scatterplot indicates that the relationship between the two variables x and y is ________.

Strong and negative

In the sample regression equation y^= b0 + b1x, What is y^?

The predicted value of y, given a specific x value

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

The tails get closer and closer to the x axis but never touch it.

What does the estimated intercept (b0) in regression analysis?

The value of the response variable when all of the explanatory variables are 0

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

Stratified sampling is generally more accurate than cluster sampling.

True

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

True

Which of the following statements about variance is the most accurate?

Variance is the average of the squared deviations from the mean.

A z-value of -1.83 represents:

a corresponding x value that falls 1.83 standard deviations below the mean

A standard normal distribution is a normal distribution with _____.

a mean of 0 and a standard deviation of 1

All of the following are discrete variables except

a person's height

As a general guideline, the research hypothesis should be stated as the:

alternative hypothesis

A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 The median is _____.

b. 6

Which of the following setups correspond to a negative, one-tailed hypothesis test?

b. Ho: μ≥ 74.5

In regression analysis, if the dependent variable is measured in dollars, the independent variable ____.

can be measure in any units

A regression model that incorporates three independent variables to explain the variation in one dependent variable is called ____.

complex

The sample variance _____.

could be smaller, equal to, or larger than the true value of the population variance

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

d. sample statistic

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 _____.

greater than 1.645

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

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

Which of the following best describes a relationship that is stochastic?

influenced by some external "noise"

Which of the following relationships might you expect to be negative?

iters of pesticide sprayed and number of insects on crops

If a hypothesis is rejected at the 5% level of significance, it _____.

may or may not be rejected at the 1% level

The median of a sample will always equal the _____.

mode, mean and 50th percentile

In general, the null and alternative hypotheses are ________.

mutually exclusive

The variance of a sample or a population cannot be _____

negative

The purpose of statistical inference is to provide information about the ____.

population based on information within the sample

The measure of variation that is influenced most by extreme values is the _____.

range

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?

selection bias

Simple linear regression analysis differs from multiple regression analysis in that _______.

simple linear regression uses only one explanatory variable

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, μstand for ________.

the mean delivery time

If the chosen significance level is α = 0.05, then ________.

there is a 5% probability of rejecting a true null hypothesis

Why do researchers use sample statistics instead of population parameters?

two answers - It is expensive to gather data on entire population and It is time consuming to gather data on entire population

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 ________.

z = -1.429

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

ε