notes 3

Suppose a sample regression equation is given by yˆ = 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 overpredict the value of y?

yˆ= 1, the model underpredicts y

Which of the following Excel functions returns the sample correlation coefficient?

CORREL

Which of the following represents an appropriate set of hypotheses?

H0:μ=0,HA:μ≠0

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

It can take on negative values.

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university's belief, how does one define the population parameter of interest?

It's the proportion of honors graduates with a GPA of 3.00 or below. (The parameter to be tested is the population proportion of honors graduates. )

When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20 = 1.95 with a corresponding p-value of 0.0653. At the 5% significance level, can you conclude that the correlation coefficient differs from zero?

No, since the p-value exceeds 0.05.

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. In testing the politician's claim, how does one define the population parameter of interest?

The current proportion of babies born out of wedlock

For a given sample size n, __________.

decreasing the probability of a Type I error α will increase the probability of a Type II error β

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

A Type II error occurs when we __________.

do not reject the null hypothesis when it is actually false

Unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression ________.

indicates whether the slope of the regression line is positive or negative

Which of the following R functions creates a linear model object?

lm

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

no error

A correlation coefficient r = −0.85 could indicate a ________.

very strong negative linear relationship (As the absolute value of the sample correlation coefficient approaches 1, the linear relationship is said to be stronger.)

When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the __________.

probability of incorrectly not rejecting the null hypothesis increases

The null hypothesis in a hypothesis test refers to __________.

the default state of nature

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: H0: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that __________.

the franchiser does not build on an acceptable site

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 __________.

the mean delivery time

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

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

Consider the following sample regression equation yˆ= 200 + 10x, where y is the supply for Product A (in 1,000s) and x is the price of Product A (in $). The slope coefficient indicates that if ________.

the price of Product A increases by $1, then we predict the supply to increase by 10,000 (The slope parameter b1 indicates that if x increases by 1 unit then y is predicted to change by b1.)

The standard error of the estimate measures ________.

the standard deviation of the random error

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

the unknown parameters

Given the augmented Phillips model: y = β0 + β1x1 + β2x2 + ε, where y = actual rate of inflation (%), x1 = unemployment rate (%), and x2 = anticipated inflation rate (%). The explanatory variable or variables in this model is (are) the ________.

unemployment rate and anticipated inflation rate

When conducting a hypothesis test concerning the population proportion, the value of the test statistic is calculated as __________.

z=P- - Po/√Po(1 − Po)/n