Stats Exam 2

A study was conducted on 64 female college athletes. The researcher collected data on a number of variables including percent body​ fat, total body​ weight, lean body​ mass, and age of athlete. The researcher wondered if total body weight​ (TBW), lean body mass​ (LBM), and/or age are significant predictors of​ % body fat. All conditions have been checked and are met and no transformations were needed. The partial technology output from the multiple regression analysis is given below. The researcher wants to determine if lean body mass is a significant predictor of​ % body fat after accounting for the effects of total body weight and age. What is the value of the​ test-statistic from the hypothesis test that will be used to answer this​ question?

-62.90 (Coefficient/SE)

If all the data points fall on the​ least-squares regression line in simple linear​ regression, what is the value of SSE? 100% 1 0 The value will be greater than​ 0, but its exact value cannot be determined without more information. LicensePoints possible: 1

0

A study was conducted on 64 female college athletes. The researcher collected data on a number of variables including percent body​ fat, total body​ weight, lean body​ mass, and age of athlete. The researcher wondered if total body weight​ (TBW), lean body mass​ (LBM), and/or age are significant predictors of percent body fat. All conditions have been checked and are met and no transformations were needed. The partial technology output from the multiple regression analysis is given below. The researcher wants to determine if at least one of total body​ weight, lean body​ mass, and/or age is a significant predictor of percent body fat. What is the value of the​ test-statistic that would be used in the hypothesis test to answer this​ question?

1577.84

A consumer research company recently reviewed 15 models of inkjet printers. They wanted to determine if there was an association between the speed of the printer​ (in pages per​ minute) and the cost per page printed​ (cents/page). Suppose the​ F-statistic in an Analysis of Variance table is 2 and the estimate of the standard deviation of the residuals is 4. What is the value of the mean squares of the regression​ model?

32 *****

What is a dummy​ variable? A variable having two possible values that are used to represent two different categories of a qualitative variable. A variable having two possible values that are used to represent three different categories of a quantitative variable. A variable that can only equal 0 or 1. A variable that has only two possible values. A variable having two possible values that are used to represent three different categories of a qualitative variable. A variable having two possible values that are used to represent two different categories of a quantitative variable.

A variable having two possible values that are used to represent two different categories of a qualitative variable.

The​ _______________ is the multiple coefficient of determination modified to account for the number of variables and the sample size. Adjusted Coefficient of Determination Adjusted Correlation Coefficient Standard Error of the Residuals Pooled Variance

Adjusted Coefficient of Determination

A study was conducted on 64 female college athletes. The technology output from the multiple regression analysis is given below. In a backwards selection process with a significance level of​ 0.05, which variable​ (if any) would be removed​ first? Age would be removed first since its​ t-statistic, from the​ t-tests testing the null hypothesis that a​ variable's coefficient is​ 0, is negative. Age would be removed first since it has the highest​ p-value, from the​ t-tests testing the null hypothesis that a​ variable's coefficient is​ 0, and its​ p-value is greater than 0.05. Height would be removed first since its​ t-statistic, from the​ t-tests testing the null hypothesis that a​ variable's coefficient is​ 0, is furthest from 0. Both height and​ % body fat would be removed first since both have​ p-values close to​ 0, from the​ t-tests testing the null hypothesis that a​ variable's coefficient is 0. None of the explanatory variables would be removed since the​ p-value from the​ F-test is close to 0.

Age would be removed first since it has the highest​ p-value, from the​ t-tests testing the null hypothesis that a​ variable's coefficient is​ 0, and its​ p-value is greater than 0.05.

We modeled the price of a car using its MPG and its manufacturing site (foreign or domestic). The regression output is provided below. Note that domestic is the reference level for manufacturing site, and that the data is somewhat old so the prices may seem too low for today's prices. What is the interpretation of the slope of manufacturing site? Coef.Std. Err.tP(t > |t|)intercept11905115910.270.000mpg-29455-5.350.000site:foreign17677002.520.014 All else held constant, the model predicts that foreign made cars cost $1,767 higher than domestic cars. All else held constant, the model predicts that foreign made cars cost $294 lower than domestic cars. As a car goes from being domestic to foreign its price increases by $1,767. Site has a small p-value, hence the manufacturing site of the car is a significant predictor of its price.

All else held constant, the model predicts that foreign made cars cost $1,767 higher than domestic cars.

An investigator conducts an experiment with four treatment groups. The response variable is growth of a plant during the experiment. She performs an​ F-test. What is the null hypothesis the researcher is testing with the​ F-test? All four treatment groups have a different average growth of plants during the experiment. All plants in all treatment groups have the same growth during the experiment. All plants in each treatment group have the same growth during the​ experiment, but plants in different treatment groups might have different growths. All four treatment groups have the same average growth of the plants during the experiment. At least one treatment group has a different average growth of plants during the​ experiment, but not all four necessarily have different mean growths.

All four treatment groups have the same average growth of the plants during the experiment.

The null hypothesis for an ANOVA is that all treatments/samples come from populations with the same mean. The alternative hypothesis is best stated as: __________ of the population means is different from the others."

At least one

An investigator conducts an experiment with four treatment groups. The response variable is growth of a plant during the experiment. She performs an​ F-test. What is the alternative hypothesis the researcher is testing with the​ F-test? All four treatment groups have the same average growth of the plants during the experiment. All four treatment groups have the same average growth of the plants during the experiment. All four treatment groups have a different average growth of plants during the experiment. All plants in each treatment group have the same growth during the​ experiment, but plants in different treatment groups might have different growths. At least one treatment group has a different average growth of plants during the​ experiment, but not all four necessarily have different mean growths.

At least one treatment group has a different average growth of plants during the​ experiment, but not all four necessarily have different mean growths.

An article compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. We are interested in finding out if the average test scores are different for the different teaching methods. The p-value of the test is 0.0168. What is the conclusion of the test? All five group means are significantly different from each other. At least two group means are significantly different from each other. At most two group means are significantly different from each other. Only two group means are significantly different from each other. LicensePoints possible: 1

At least two group means are significantly different from each other.

Which statement below describes the hypotheses for a​ two-way ANOVA​ test? A​ two-way ANOVA test has two null​ hypotheses, one for the main effect and one for the interaction effect. The null hypothesis for a​ two-way ANOVA test is that all population means are equal. The alternative hypothesis is that at least one population mean is different. The null hypothesis for a​ two-way ANOVA test is that the main effect is due to the independent variable. The alternative hypothesis is that the main effect is due to interaction. A​ two-way ANOVA test has three null​ hypotheses, one for each main effect and one for the interaction effect.

A​ two-way ANOVA test has three null​ hypotheses, one for each main effect and one for the interaction effect.

We would like to test if students who are in the social sciences, natural sciences, arts & humanities, and other fields spend the same amount of time. on average, studying for this course. What type of test should we use? t-test for two independent groups z-test F-test (ANOVA) chi-square test t-test for two dependent groups

F-test (ANOVA)

A consumer research company recently reviewed 15 models of inkjet printers. They wanted to determine if there was an association between the speed of the printer​ (in pages per​ minute) and the cost per page printed​ (cents/page). An​ F-test can be used to answer the question of interest of whether or not speed is a significant predictor of cost. In​ general, the smaller the​ F-statistic, the more evidence there is to reject the null hypothesis. Is this statement true or​ false? False True

False

Mark the statement True or False. If you believe that a statement is​ false, briefly explain why you think it is false. If we reject Ho​: β1 = β2 =0 using the​ F-test, then we should conclude that both slopes are different from zero. Choose the correct answer below: ​False, because it is possible only one differs from zero. True ​False, because both slopes equal zero.

False, because it is possible only one differs from zero.

In​ regression, a residual can be negative. Is this statement true or​ false? False, residuals are always squared and thus are never negative. True, if the y-value of the data point is less than the predicted value, the residual will be negative False, if the y-value of the data point is less than the predicted value, the residual will be positive. True, if the y-value of the data point is greater than the predicted value, the residual will be negative.

False, if the y-value of the data point is less than the predicted value, the residual will be positive.

Which hypotheses below are for a​ one-way ANOVA​ test? H0​: All population means are equal.Ha​: None of the population means are equal. H0​: All population means are equal.Ha​: At least one population mean is different from the others. H0​: None of the population means are equal.Ha​: All population means are equal. H0​: At least one population mean is different from the others.Ha​: All population means are equal.

H0​: All population means are equal.Ha​: At least one population mean is different from the others.

Which of the following is false? If the correlation coefficient is 1, then the slope must be 1 as well. Correlation coefficient and the slope always have the same sign (positive or negative). Correlation measures the strength of linear association between two numerical variables. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them.

If the correlation coefficient is 1, then the slope must be 1 as well.

Sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC) in grams of alcohol per deciliter of blood. Given is a scatterplot displaying the relationship between BAC and number of cans of beer as well as the linear model for predicting BAC. If the student who drank the most number of beers (9 beers) actually had a BAC of 0.15 grams/deciliter, how would the strength of the association change?

Increase

If SSR = 120, why is it impossible for SST to equal​ 110? It is impossible because SST cannot be less than - 100 or greater than 100. It is impossible because SSE = SSR + SST and a sum of squares cannot be negative. It is impossible because SST = SSR + SSE and a sum of squares cannot be negative. It is impossible because SST = ​2(SSR).

It is impossible because SST = SSR + SSE and a sum of squares cannot be negative.

The simple linear regression model is y =βo+ β1x What does β1 represent? It is the observed value of the response variable for the ith observation in the population. It is the​ y-intercept of the population regression line. It is the slope of the population regression line. It is the residual of the ith observation in the population. It is the value of the explanatory variable for the ith observation in the population.

It is the slope of the population regression line.

Which of the following statements are true when creating an approximate linear model for a given data set? Check all that apply.It can only be done if the data is perfectly linear.It provides a way to make predictions on data points outside the given data setIt is called Linear RegressionIt is called Finding the Line of Best Fit

It provides a way to make predictions on data points outside the given data set It is called Linear Regression It is called Finding the Line of Best Fit

According to the model, if an owner remodels the apartment and as a consequence itscondition improves by 2, what should happen to the estimated rent? it should increase by $105.798 the estimated rent would not change it should decrease by $53.899 it should increase by $53.899 it should decrease by $105.798 Suppose you have your eye on a two-bedroom apartment that has 2 bathrooms, itscondition is 3, the quality of the neighborhood is 4, and it is located 1 mile from theQuad. How much should you expect to pay in rent? $1358.228 $900.92 $272.414 $968.897 $1036.874

It should increase by $105.798 $900.92 MAKE SURE TO SUBTRACT Y INTERCEPT

If an observation has a residual of​ 0, which of the following statements is​ true? It is an outlier. The​ R-square will be 1. The correlation coefficient will be 0. An error was made in the calculation as a residual cannot be zero. Its predicted value is the same as its observed value.

Its predicted value is the same as its observed value.

Describe the difference between the variance between samples (MSB) and the variance within samples (MSW). MSW measures the differences related to the treatment given to each sample.MSB measures the differences related to entries within the same sample. MSB measures the differences related to the treatment given to each sample.MSW measures the differences related to entries within the same sample. MSB measures the differences related to the treatment given to each sample.MSW measures the differences related to the grand mean. MSB measures the differences related to the grand mean.MSW measures the differences related to entries within the same sample.

MSB measures the differences related to the treatment given to each sample.MSW measures the differences related to entries within the same sample.

What value is the pooled variance in the Analysis of Variance​ table? SSE^2 MSE SSE MSE^2 sqrt(MSE)

MSE

A regression analysis was performed to determine​ which, if​ any, of protein​ (grams), total fat​ (grams), fiber​ (grams), carbohydrates​ (grams), and sugars​ (grams) are associated with calories in a sample of 34 breakfast cereals. Which of the following is the null hypothesis for the​ F-test in this​ problem? Exactly one of​ protein, total​ fat, fiber,​ carbohydrates, or sugars helps to explain calories in breakfast cereals. At least one of​ protein, total​ fat, fiber,​ carbohydrates, or sugars helps to explain calories in breakfast cereals. All of​ protein, total​ fat, fiber,​ carbohydrates, or sugars help to explain calories in breakfast cereals. None of​ protein, total​ fat, fiber,​ carbohydrates, or sugars helps to explain calories in breakfast cereals.

None of​ protein, total​ fat, fiber,​ carbohydrates, or sugars helps to explain calories in breakfast cereals.

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were: y=ax+b a=-1.178 b=26.572 r2=0.430336 r=-0.656 Use this to predict the number of situps a person who watches 12 hours of TV can do (to one decimal place)

Plug it in! 12.4

A study was conducted on 64 female college athletes. The researcher collected data on a number of variables including percent body​ fat, total body​ weight, height, and age of athlete. The researcher wondered if​ % body fat​ (%BF), height​ (HGT), and/or age are significant predictors of total body weight. All conditions have been checked and are met and no transformations were needed. The technology output from the multiple regression analysis is given below. If age was removed from the​ model, what would happen to​ R-square? R-square would stay the same since age was not a significant predictor of total body weight. R-square would go up since age was not a significant predictor of total body weight. More information is needed to determine what would happen to​ R-square if age was removed. R-square would go down or stay the​ same, but would not go up.

R-square would go down or stay the​ same, but would not go up.

If we use the amounts​ (in millions of​ dollars) grossed by movies in categories with​ PG, PG-13, and R​ ratings, we obtain the analysis of variance results shown below. Use a 0.01 significance level to test the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount. Fail to reject Ho. There is sufficient evidence to warrant the rejection of the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount Fail to reject Ho. There is insufficient evidence to warrant the rejection of the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount Reject Ho. There is insufficient evidence to warrant the rejection of the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount. Reject Ho. There is sufficient evidence to warrant the rejection of the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount.

Reject Ho. There is insufficient evidence to warrant the rejection of the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount.

In multiple​ regression, an explanatory variable is highly correlated with all other explanatory variables. What should be​ done? Remove the explanatory variable that is highly correlated with all other explanatory variables. Remove the response variable that is highly correlated with all other response variables. Perform an analysis with and without the explanatory variable that is highly correlated with the other explanatory variables and report the results of both analyses. Remove all of the other explanatory variables.

Remove the explanatory variable that is highly correlated with all other explanatory variables.

An experiment was performed to look at the reflectivity of different paints used on roads. Four paints were used​ (call them Paint​ 1, Paint​ 2, Paint​ 3, and Paint​ 4). Twenty-four sections of roads with similar travel patterns and weather patterns were used. Each type of paint was randomly assigned to one of the 24 sections of road so that each paint type was used on 6 different road sections. The percent of reflectivity after 6 months was determined and recorded. What is the value of the pooled variance (MSE)?

S=6.237 so square it! 38.9

If all the data points fall on the​ least-squares regression line in simple linear​ regression, which of the following is​ true? MSR = 100% SS(Total) = 0 SSR = SST F-statistic = 0 None of the above statements are true.

SSR = SST

What is the test statistic corresponding to the claim that there is a significant correlation? enter 3 decimal places What is the test statistic for the overall validity of the model? enter 3 decimal places What is the best estimate for the pooled variance? enter 3 decimal places

See last page of excel

Which of the following is NOT true when using​ one-way analysis of variance for testing equality of three or more population​ means? The conclusion that there is sufficient evidence to reject the claim of equal population means does not indicate a particular mean is different from the others. Small​ P-values indicate that the decision is to reject the null hypothesis of equal means. Small F test statistics indicate that the decision is to reject the null hypothesis of equal means. This is the correct answer. The numerator of the F test statistic measures variation between sample means.

Small F test statistics indicate that the decision is to reject the null hypothesis of equal means. This is the correct answer.

A multiple regression analysis is being performed. No explanatory variables are highly correlated and there are no outliers. All the conditions of the multiple regression model are met. There is no evidence to reject the null hypothesis from the​ F-test. What should be done​ next? Stop the analysis as all explanatory variables are significant predictors of the response variable. Do the​ F-test again on each explanatory variable to determine if each explanatory variable is a significant predictor of the response variable. Stop the analysis as none of the explanatory variables are significant predictors of the response variable.

Stop the analysis as none of the explanatory variables are significant predictors of the response variable.

Which of the following is NOT a property of the F​ distribution? The F distribution is bell shaped. The exact shape of the F distribution depends on the two different degrees of freedom. Values in the F distribution cannot be negative. The F distribution is not symmetric.

The F distribution is bell shaped.

Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable​ increases? The dependent variable decreases. The dependent variable increases.

The dependent variable increases.

Use the image below to help you describe the Explained Variation in words The explained variation is the sum of the squares of the differences between the​ y-values of each ordered pair and the mean of the​ y-values of the ordered pairs The explained variation is the sum of the squares of the differences between the predicted​ y-values and the mean of the​ y-values of the ordered pairs. The explained variation is the sum of the squares of the differences between the observed​ y-values and the predicted​ y-values.

The explained variation is the sum of the squares of the differences between the predicted​ y-values and the mean of the​ y-values of the ordered pairs.

A golfer wants to determine if the type of equipment used every year can be used to predict the amount of improvement in his game.

The explanatory variable is the type of equipment used and the response variable is the amount of improvement in his game.

What does it mean to say​ "correlation does not imply​ causation"? The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables. Two variables can only be strongly correlated if there existed a​ cause-and-effect relationship between the variables. The fact that two variables are strongly correlated implies a​ cause-and-effect relationship between the variables. Two variables that have a​ cause-and-effect relationship are never correlated.

The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

A random sample of 200 women who were at least 21 years old, of Pima Indian heritage and living near Phoenix, Arizona, were tested for diabetes according to World Health Organization criteria. The model below is used for predicting their plasma glucose concentration based on their diastolic blood pressure (in mmHg), age (in years), and whether or not they are diabetic. Which of the following statements is false? EstimateStd. Err.tP(t > |t|)intercept76.0012.246.23e-09bloodpressure0.350.181.90.05age0.430.202.10.04diabetes_Yes26.574.376.16e-09 Residual standard error: 27 on 196 degrees of freedom Multiple R-squared: 0.28, Adjusted R-squared: 0.27 F-statistic: 25 on 3 and 196 DF, p-value: 1e-13 The model as a whole is significant, even though one of the variables (blood pressure) may not be. The predicted difference in blood glucose levels of two 25 year old females who don't have diabetes one of whom has a blood pressure of 70mmHg and the other 75 mmHG is 0.35 * 5 = 1.75. The model predicts that women without diabetes have blood glucose levels that are on average 26.57 higher than those who have diabetes, given that they are similar in terms of their blood pressure and age. The model explains 28% of variability in blood glucose levels of these women.

The model predicts that women without diabetes have blood glucose levels that are on average 26.57 higher than those who have diabetes, given that they are similar in terms of their blood pressure and age.

Describe the range of values for the correlation coefficient. The range of values for the correlation coefficient is -1 to​ 1, not inclusive. The range of values for the correlation coefficient is 0 to​ 1, not inclusive. The range of values for the correlation coefficient is -1 to​ 1, inclusive. The range of values for the correlation coefficient is 0 to​ 1, inclusive.

The range of values for the correlation coefficient is -1 to​ 1, inclusive.

What is the relationship between the linear correlation coefficient r and the slope of a regression​ line with one independent variable? The value of r will always have the same sign as the value of the slope The value of r will always be larger than the value of the slope. The value of r will always have the opposite sign of the value of the slope. The value of r will always be smaller than the value of the slope.

The value of r will always have the same sign as the value of the slope

An experiment was performed to look at the reflectivity of different paints used on roads. Four paints were used​ (call them Paint​ 1, Paint​ 2, Paint​ 3, and Paint​ 4). Twenty-four sections of roads with similar travel patterns and weather patterns were used. Each type of paint was randomly assigned to one of the 24 sections of road so that each paint type was used on 6 different road sections. The percent of reflectivity after 6 months was determined and recorded. Which of the following can we conclude based on the​ F-test? There is conclusive evidence to indicate that at least one paint type is a significant predictor of reflectivity 6 months later. There is conclusive evidence to indicate that at least one paint type has a different mean reflectivity 6 months later than the other paint types. There is conclusive evidence to indicate that all paint types have the same mean reflectivity 6 months later. There is conclusive evidence to indicate that all paint types have different mean reflectivity 6 months later. There is not enough evidence to indicate that all paint types have different mean reflectivity 6 months later.

There is conclusive evidence to indicate that at least one paint type has a different mean reflectivity 6 months later than the other paint types.

A study was conducted on 64 female college athletes. The technology output from the multiple regression analysis is given below. Which of the following is a correct conclusion testing Ho: β2=0​, where β2 is the coefficient for​ height? There is enough evidence to indicate that height is a significant predictor of total body weight after accounting for the effects of​ % body fat and age in the regression model (t-statistic = 9.32, ​p-value < 0.001) There is strong evidence to indicate that height is a significant predictor of total body weight after accounting for the effects of​ % body fat and age in the regression model​ (F-statistic =​ 40.48, ​p-value < ​0.001) For a certain individual with a given height and​ age, there is strong evidence to indicate that height is a significant predictor of total body weight​ (t-statistic =​ 9.32, ​p-value < ​0.001) There is not enough evidence to indicate that height is a significant predictor of total body weight after accounting for the effects of​ % body fat and age in the regression model (t-statistic = 9.32, ​p-value < 0.001) For a certain individual with a given height and​ age, there is not enough evidence to indicate that height is a significant predictor of total body weight​ (F-statistic =​ 40.48, ​p-value < 0.001)

There is enough evidence to indicate that height is a significant predictor of total body weight after accounting for the effects of​ % body fat and age in the regression model (t-statistic = 9.32, ​p-value < 0.001)

What does a correlation coefficient of 0​ indicate? It indicates a calculation​ error, as the correlation coefficient cannot be 0. There is no linear relationship between the two quantitative variables. There is a weak relationship between the two quantitative variables. There is a strong relationship between the two quantitative variables. It indicates a​ non-linear relationship between the two quantitative variables.There is no linear relationship between the two quantitative variables.

There is no linear relationship between the two quantitative variables.

A regression analysis was performed to determine​ which, if​ any, of protein​ (grams), total fat​ (grams), fiber​ (grams), carbohydrates​ (grams), and sugars​ (grams) are associated with calories in a sample of 34 breakfast cereals. Suppose the​ P-value from the Analysis of Variance F-test = 0.005. Which of the following is the correct​ conclusion? There is strong evidence to indicate that at least one of these explanatory variables help to explain calories in breakfast cereals. There is strong evidence to indicate that exactly one of these explanatory variables help to explain calories in breakfast cereals. There is strong evidence to indicate that all of these explanatory variables help to explain calories in breakfast cereals. There is not enough evidence to indicate that all of these explanatory variables help to explain calories in breakfast cereals. There is not enough evidence to indicate that any of these explanatory variables help to explain calories in breakfast cereals.

There is strong evidence to indicate that at least one of these explanatory variables help to explain calories in breakfast cereals.

If all observations have a residual of​ 0, which of the following statements is​ true? An error was made in the calculation as a residual cannot be zero. The slope of the regression line will be 1. The​ R-square will be 1. The correlation coefficient will be 0.

The​ R-square will be 1.

Independent samples t-tests are limited to situations in which there are only 2 treatments being compared. This chapter looks at tests where _________ or more means are involved.

Three

Alex calculated a correlation coefficient of −1.5. He made a mistake in his calculation since the correlation coefficient has to be between −1 and 1. True False

True

Select all the charts that violate the conditions for linear regression.

bcdef

An article compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. Which of the following is the correct degrees of freedom for an F-test for evaluating if the average test scores are different for the different teaching methods?

dfG = 4, dfE = 40

A regression analysis was performed to determine​ which, if​ any, of protein​ (grams), total fat​ (grams), fiber​ (grams), carbohydrates​ (grams), and sugars​ (grams) are associated with calories in a sample of 34 breakfast cereals. An​ F-test is to be performed. How many degrees of freedom does the​ F-statistic have? numerator = ​5, denominator = 28 numerator = ​3, denominator = 30 numerator = ​4, denominator = 30 numerator = ​3, denominator = 31 numerator = ​1, denominator = 32

numerator = ​5, denominator = 28

The scatterplot below shows the relationship between poverty rate in the 51 states in the US (including DC) and percentage of households with a female head (no husband present). The average poverty rate is 11.35% with a standard deviation of 3.1% and the average percentage of households with a female head is 11.63% with a standard deviation of 2.36%. The correlation between these variables is 0.53. Which of the below is the correct linear model for predicting poverty rate from percentage of households with a female head.

poverty = 3.2 + 0.7 * female_household

Discuss the difference between r and ρ. r is the sample correlation coefficient and ρ is the population correlation coefficient. r is the sample coefficient of determination and ρ is the population coefficient of determination. r is the population correlation coefficient and ρ is the sample correlation coefficient. r is the population coefficient of determination and ρ is the sample coefficient of determination.

r is the sample correlation coefficient and ρ is the population correlation coefficient.

Note that a significantly large F-ratio is evidence against equal population means. In other words, significantly large F-ratios support the alternative hypothesis that "at least one mean is different". Thus, ANOVA hypothesis tests are always ____-tailed.

right

The ANOVA procedure is a statistical approach for determining whether or not... the means of more than two populations are equal the means of more than two populations are not equal the means of more than two samples are equal the means of more than two samples are not equal None of the above are true

the means of more than two populations are equal

The ANOVA procedure is a statistical approach for determining whether or not... the means of more than two populations are equal the means of more than two samples are not equal the means of more than two samples are equal the means of more than two populations are not equal None of the above are true

the means of more than two populations are equal

The​ F-statistic in a​ one-way Analysis of Variance problem has how many numerator degrees of​ freedom? the total sample size of all groups combined minus 1. the total sample size of all groups combined minus the number of groups being compared minus 1. the number of groups being compared minus 1. the number of groups being compared. the total sample size of all groups combined minus the number of groups being compared

the number of groups being compared minus 1

The​ F-statistic in a​ one-way Analysis of Variance problem has how many denominator degrees of​ freedom? the total sample size of all groups combined minus the number of groups being compared minus 1. the total sample size of all groups combined minus 1. number of groups being compared minus 1. number of groups being compared. the total sample size of all groups combined minus the number of groups being compared.

the total sample size of all groups combined minus the number of groups being compared.

If you wanted to test whether the correlation coefficient (ρ) between childs' educationand mothers' education was statistically different from zero, what information wouldyou use? t-stat = 2.915, p-value = .004 t-stat = 1.126, p-value = 0.263 t-stat = 7.953, p-value = 3.57E-12 F-stat = 10.147, p-value = 7.23E-06 this test cannot be performed with the given information If you wanted to test whether the variable of gender has a significant impact on a childs' education what information wouldyou use? t-stat = 1.126, p-value = 0.263 F-stat = 10.147, p-value = 7.23E-06 t-stat = -0.837, p-value = 0.404 t-stat = 2.915, p-value = .004 this test cannot be performed with the given information Using a step-wise regression to build a model, which variable (if any) would be removed first? Mother Father Gender none would be removed How many total observations are in this data set? How many independent variables are in this data set? What is the denominator degrees of freedom for the test of the overall significance of the regression? If we removed one of the variables from the model (does not matter which), what are we sure would happen? we are sure that R2 will not decrease we are sure that adjusted R2 will not decrease we are sure that adjusted R2 will not increase we are sure that R2 will not increase none of the above

this test cannot be performed with the given information t-stat = -0.837, p-value = 0.404 we are sure that R2 will not increase