Eco 391 final pt 2

A machine that is programmed to package 1.202 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct? Assume a CI of 95%.

The machine is operating properly because the interval contains the target.

Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. With the beginning of the next academic year, all professors will get a 2% raise. What will be the average and the standard deviation of their new salaries?

$81,600 and $6,120.

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ________.

0.0957

For a multiple regression model, SSE = 600 and SSR = 200. The coefficient of determination (R2) is _____.

0.250

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240 (Sum of Squares of the Errors). The coefficient of determination is ______.

0.700

The yearly income of a 24-year-old male individual is _____.

46,800

The yearly income of a 24-year-old female individual is _____.

49,800

How can autocorrelation occur?

If you omit an important variable with some degree of persistence

A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000.Provide a 95% confidence interval estimate for the average daily sale.

It has a lower bound of $194,120 and an upper bound of $205,880

Construct a 95% confidence interval for the mean monthly electric bills of all residents.

It has a lower bound of $87.06 and an upper bound of $92.94

If the variance of the error term is not the same for all observations, we ________.

cannot conduct tests of significance (t-tests)

As the sample size increases, the margin of error _____.

decreases

Consider the following competing hypotheses: H0: 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

When confronted with multicollinearity, a good remedy is to ________ if we can justify its redundancy.

drop one of the collinear variables

Use the following scenario to answer questions 22 and 23 below: a. Y = β0 + β1X1 + β2X2 + ε b. E(y) = β0 + β1X1 c. Y = β0 + β1X1 + β2X2 d. E(y) = β0 + β1X1 + β2X2 Which equation describes the multiple regression model?

equation a

a. Y = β0 + β1X1 + β2X2 + ε b. E(y) = β0 + β1X1 c. Y = β0 + β1X1 + β2X2 d. E(y) = β0 + β1X1 + β2X2 Which equation gives the estimated regression line?

equation c

Consider the regression model Y = β0 + β1X + β2D + β3XD + ε. If the dummy variable D changes from 0 to 1, the estimated changes in the intercept and the slope are β0 + β2 and β2 respectively.

false

For the model ln(y) = β0 + β1x + ε, β1 is the approximate percentage change in y when x increases by 1%.

false

For the model y = β0 + β1ln(x) + ε, β1 is the approximate percentage change in y when x increases by 1%.

false

On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis."

false

The term multicollinearity refers to the condition when the variance of the error term, of x1, x2, ..., xn, is the same for all observations.

false

When some explanatory variables of a regression model are strongly correlated, this phenomenon is called autocorrelation.

false

Use the following scenario to answer questions 29 to 31 below: The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (X1) and their gender (X2) (0 if male and 1 if female). Y = 30 + 0.7 X1 + 3 X226 From the above function, it can be said that the expected yearly income for _____.

female is $3,000 more than males

A regression model between sales (y in $1000s), unit price (X1 in dollars) and television advertisement (X2 in dollars) resulted in the following function: Y= 7 - 3X1 + 5X249. The coefficient of X2 indicates that if television advertising is increased by $1 (holding the unit price constant), sales are expected to _____.

increase by $5,000

A multiple regression model has the form Y = 7 + 2 X1 + 9 X2 As X1 increases by 1 unit (holding X2 constant), Y is expected to _____.

increase by 2 units

In a multiple regression model, the values of the error term, ε, are assumed to be _____.

independent of each other

The average monthly electric bill of a random sample of 256 residents of a city is $90. The population standard deviation is assumed to be $24.30. Construct a 90% confidence interval for the mean monthly electric bills of all residents.

it has a lower bound of $87.53 and an upper bound of $92.46

in an accounting class of 200 students, the mean and standard deviation of scores was 70 and 5, respectively. Use the empirical rule to determine the number of students who scored less than 65 or more than 75.

it is about 64

The number of dummy variables representing a qualitative variable should be ______.

one less than the number of categories of the variable

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called a(n) _____.

qualitative variable

. 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

The adjusted multiple coefficient of determination (the adjusted R2 (𝑅2)) is adjusted for _____.

the number of independent variables

As the goodness of fit for the estimated multiple regression equation increases, _____.

the value of the multiple coefficient of determination increases

Multicollinearity is suspected when ________.

there is a high R2 coupled with insignificant explanatory variables

In general, higher confidence levels provide _____.

wider confidence intervals

For the model ln(y) = β0 + β1x + ε, if x increases by one unit, then Y changes by approximately

β1 × 100%

What is the decision rule when using the p-value approach to hypothesis testing?

Reject H0 if the p-value < α.

Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bell-shaped. What can be said about the percentage of salaries that are less than $68,000 or more than $92,000?

Its about 5%