Statistics Final

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male), and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results: Based on the hypothesis tests for the individual regression coefficients, _______.

"job" is the only nonsignificant variable in the model

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male), and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results: Based on the hypothesis tests for the individual regression coefficients, _______.

"job" is the only nonsignificant variable in the model

The average cost of tuition plus room and board for a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the critical z-value for this test?

+1.645

Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level. The value of t is _______.

+1.685

The average cost of tuition plus room and board at for a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the test statistic for this test?

+3.82

If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?

0

What is the probability of making a Type II error if the null hypothesis is actually true?

0

What is the range of values for the coefficient of determination?

0% to 100% inclusive

The average cost of tuition plus room and board for a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the p-value for this test?

0.0000

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the standard error of the slope?

0.176

Consider the following regression equation: Y = 30 + 8X. If SSE = 720 and SS Total = 1,200, then the correlation coefficient is _______.

0.632

Consider a multiple regression analysis involving 14 independent variables and 150 observations, with SSE = 180 and SS Total = 600. The coefficient of multiple determination is _______.

0.70

What does the coefficient of determination equal if r = 0.89?

0.7921

Using the following information: What is the correlation coefficient?

0.9583

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample standard deviation?

1.177

Consider a two-tailed test with a level of confidence of 80.30%. The z-value is _______.

1.29

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample variance?

1.386

Using a 5% level of significance and a sample size of 25, what is the critical t-value for a null hypothesis, H0: µ ≤ 100?

1.711

Using the following information: What is the standard error of the estimate?

11.6985

If the coefficient of multiple determination is 0.81, what percent of variation is not explained?

19%

In a regression analysis, three independent variables are used in the equation based on a sample of 40 observations. In the ANOVA table for a multiple regression analysis, what are the degrees of freedom associated with the F statistic?

3 and 36

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which result in the following function: Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4 For this model, there were 35 observations; SSR = 1,400 and SSE = 600. The critical F-value at the 1% level of significance is

4.02

A regression analysis yields the following information: Yˆ=2.21+1.49X;n=10;Sy,x=1.66;∑X2=32;∑(x−x)2=31.6Y^=2.21+1.49X;n=10;Sy,x=1.66;∑X2=32;∑(x-x)2=31.6 Compute the 95% prediction interval when X = 4.

4.118, 12.226

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: X=33.4 ∑(X−X)2=2814.4.X=33.4 ∑(X-X)2=2814.4. Rounding to one decimal place, the 95% confidence interval for 30 calls is _______.

46.7, 60.6

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: X=33.4 ∑(X−X)2=2814.4.X=33.4 ∑(X-X)2=2814.4. Rounding to one decimal place, the 95% confidence interval for 30 calls is _______.

46.7, 60.6

A machine is set to fill the small-size packages of M&M candies with 56 candies per bag. A sample revealed three bags of 56, two bags of 57, one bag of 55, and two bags of 58. To test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?

7

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample mean?

7.6

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: What is the value of the standard error of estimate?

9.310

Using the following information: If testing the hypothesis H0: ρ = 0, the computed t statistic is __________.

9.49

Using the following information: What is the coefficient of determination? Round the percentage to one decimal point.

91.8%

Using the following information: The regression analysis can be summarized as follows:

A significant positive relationship exists between the variables.

In hypothesis testing, what is the level of significance?

All of the answers apply.

If the correlation between the two independent variables of a regression analysis is 0.11, and each independent variable is highly correlated to the dependent variable, what does this indicate?

An effective regression equation.

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decided to use the 0.10 significance level. For what values of t will the null hypothesis not be rejected?

Between −1.761 and 1.761

Chapter 13

Chapter 13

Chapter 14

Chapter 14

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. What is this table called?

Correlation matrix

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. What is this table called?

Correlation matrix

What statement do we make that determines if the null hypothesis is rejected?

Decision rule

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.05, what conclusion should be drawn?

Do not reject the null hypothesis as the test statistic is less than the critical value of z.

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the decision rule?

Do not reject the null hypothesis if computed z lies between −1.645 and +1.645; otherwise, reject it.

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which independent variable has the strongest association with the dependent variable?

Education

Which statistic is used to test a global hypothesis about a multiple regression equation?

F

Consider a regression model involving more than one independent variable. The test used to determine if the relationship between the dependent variable and the set of independent variables is significant is the _______.

F test

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?

Fail to reject the null hypothesis.

Final Exam Review

Final Exam Review

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male), and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results: In the regression model, which of the following are dummy variables?

Gender and job

The average cost of tuition plus room and board for a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. Based on the computed test statistic or p-value, what is our decision about the average cost?

Greater than $8,500

For a two-tailed test with a 0.05 significance level, where is the rejection region when n is large and the population standard deviation is known?

Greater than +1.960 and less than −1.960

What is the null hypothesis to test the significance of the slope in a regression equation?

H0: β = 0

The best example of a null hypothesis for a global test of a multiple regression model is _______.

H0: β1 = β2 = β3 = β4 = 0

The best example of an alternate hypothesis for a global test of a multiple regression model is _______.

H1: Not all the βi's are equal to 0.

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis?

H1: µ ≠ $50,000

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the alternate hypothesis?

H1: µ ≠ 6.6

A researcher is studying the effect of 10 different variables on a critical measure of business performance. In selecting the best set of independent variables to predict the dependent variable, the stepwise regression technique is used. How are variables selected for inclusion in the model?

Highest increase in the multiple R2

For an alternative hypothesis: µ > 6,700, where is the rejection region for the hypothesis test located?

In the right or upper tail

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which is the dependent variable?

Income

Which of the following statements about stepwise regression is true?

It is a step-by-step method that adds independent variables one by one in order to build a more efficient regression equation.

If we reject the null hypothesis, H0: ρ = 0 , what can we conclude about the population correlation coefficient?

It is not zero.

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which independent variable has the weakest association with the dependent variable?

Job

A researcher is studying the effect of 10 different variables on a critical measure of business performance. A multiple regression analysis including all 10 variables is performed. What criterion could be used to eliminate 1 of the 10 variables?

Largest p-value

If the coefficient of determination is 0.94, what can we say about the relationship between two variables?

Ninety-four percent of the total variation of the dependent variable is explained by the independent variable.

What can we conclude if the global test of regression does not reject the null hypothesis?

No relationship exists between the dependent variable and any of the independent variables.

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?

Number of contacts

If a data set of 10 observations is used in a multiple regression analysis with 10 independent variables, then _______.

R2 will be equal to 1.0

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?

Reject the null hypothesis and conclude the mean is greater than 6.6 pounds.

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign, a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history, the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.05, have sales increased as a result of the advertising campaign?

Reject the null hypothesis and conclude the mean is higher than $6,000 per day.

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which result in the following function: Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4 For this model, there were 35 observations; SSR = 1,400 and SSE = 600. Assume a 0.01 significance level. Based on the given information, which of the following conclusions is correct?

Reject the null hypothesis that X1 = X2 = X3 = X4 = 0.

If we reject the null hypothesis, what can we conclude subject to the probability, α?

Reject the null with a probability, α, of making a Type I error.

What is another name for the alternate hypothesis?

Research hypothesis

Consider a regression and correlation analysis where r2 = 1. We know that _______.

SSE must equal to zero

Which of the following is not one of the six steps in the hypothesis testing procedure?

Select a level for β.

A researcher is studying the relationship between 10 different variables and a critical measure of business performance. What method can be used to select the best set of variables to predict performance?

Stepwise regression

What does a coefficient of correlation of 0.70 infer?

The coefficient of determination is 0.49.

A multiple regression model includes the term (X1)(X2). If the hypothesis concerning the term's regression coefficient is not rejected, what is a valid conclusion?

The effect of X1 on the dependent variable is independent of the value of X2.

In the regression equation, what does the letter b represent?

The slope of the line

What happens as the scatter of data values about the regression plane increases?

The standard error of estimate increases.

If the correlation coefficient between two variables, X and Y, equals zero, what can be said of the variables X and Y?

The variables are not related.

When does multicollinearity occur in a multiple regression analysis?

When the independent variables are highly correlated

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218, and 218. Using α = 0.025, has the shelf life of the cake mix increased?

Yes, because computed t is greater than the critical value.

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths in millimeters recorded. The lengths (in millimeters) are 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. If the computed t = −2.913, has there been a statistically significant change in the mean length of the bars?

Yes, because the computed t lies in the rejection region.

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the regression equation?

YˆY^ = −12.201 + 2.195X

Multiple regression analysis is applied when analyzing the relationship between _______.

a dependent variable and several independent variables

A variable that can assume only one of two possible outcomes that take on the values of either 0 or 1, and is used to incorporate the effect of qualitative variables in a regression model, is referred to as _______.

a dummy variable

In multiple regression analysis, a dummy variable is _______.

a nominal variable with only two values

In multiple regression analysis, testing the global null hypothesis that all regression coefficients are zero is based on _______.

an F statistic

A multiple regression model includes (X1)(X2). The term is called _______.

an interaction

An example of a way to rescale a variable to create a linear relationship is ______.

computing the log of all values of the dependent and independent variables

The variance inflation factor can be used to reduce multicollinearity by _______.

eliminating variables for a multiple regression model

In multiple regression analysis, residuals (Y−Ŷ) are used to _______.

evaluate homoscedasticity

The coefficient of determination measures the proportion of _______.

explained variation relative to total variation

In multiple regression analysis, residuals (Y − Ŷ) should be _______.

normally distributed with a mean of zero

A null hypothesis makes a claim about a _______.

population parameter

Based on the regression equation, we can _______________.

predict the value of the dependent variable given a value of the independent variable

In an ANOVA table for a multiple regression analysis, total variation is separated into _______.

regression and residual variation

In an ANOVA table for a multiple regression analysis, the global test of significance is based on the _______.

regression mean square divided by the mean square error

To evaluate the assumption of linearity, a multiple regression analysis should include _______.

scatter diagrams of the dependent variable plotted as a function of each independent variable

Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05; therefore, the null hypothesis _______.

should not be rejected

If the correlation between two variables is close to one, the association between the variables is ___________.

strong

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level?

t = ±2.179

The regression equation is Ŷ = 29.29 − 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the critical value to test the significance of the slope at the 0.01 significance level?

t = ±3.707

The regression equation is Ŷ = 29.29 − 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the test statistic to test the significance of the slope?

t = −4.364

What is the test statistic to test the significance of the slope in a regression equation?

t statistic

Which statistic is used to test hypotheses about individual regression coefficients?

t statistic

In the least squares equation, Ŷ = 10 + 20X, the value of 20 indicates ____________.

that Y increases by 20 units for each unit increase in X

In regression, the difference between the confidence interval and prediction interval formulas is _______.

the addition of 1 to the quantity under the radical sign

When comparing the 95% confidence and prediction intervals for a given regression analysis ______________.

the confidence interval is narrower than a prediction interval

The probability of a Type II error is directly related to _______.

the difference between the hypothesized mean and the critical value of the sample mean

A multiple regression model includes the term (X1)(X2). The term implies that _______.

the effect of X1 on the dependent variable may depend on the value of X2

A valid multiple regression analysis assumes or requires that _______.

the independent variables and the dependent variable have a linear relationship

In multiple regression analysis, before testing the significance of the individual regression coefficients, _______.

the null hypothesis that all regression coefficients equal zero must be rejected

To conduct a test of hypothesis with a small sample, we make an assumption that __________.

the population is normally distributed

Which symbol represents a test statistic used to test a hypothesis about a population mean?

z

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the critical value?

±1.645

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. If α = 0.05, what is the critical t-value?

±2.447

What is the general form of the regression equation?

Ŷ = a + (bX)

Using the following information: The regression equation is _______.

Ŷ = −12.8094 + 2.1794X

For a one-tailed hypothesis test, the critical z-value of the test statistic is −2.33. Which of the following is true about the hypothesis test?

α = 0.01 for a lower-tailed test

The probability of a Type II error is represented by _______.

β

Which value of r indicates a stronger correlation than 0.40?

−0.80

Consider a left-tailed test, where the p-value is found to be 0.10. If the sample size n for this test is 49, then the t-statistic will have a value of _______.

−1.299

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the Y-intercept of the linear equation?

−12.201

Using the following information: Estimate the value of Ŷ when X = 4.

−4.092