Q&A Hero

Q: The sum of the residuals in a least squares regression model will be zero only when the correlation between the x and y variables is statistically significant.

Q: If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.

Q: You are given the following sample data for two variables: Y X 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 The regression model based on these sample data explains approximately 75 percent of the variation in the dependent variable.

Q: Given a sample of data for use in simple linear regression, the values for the slope and the intercept are chosen to minimize the sum of squared errors.

Q: In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Based on this model, the expected utility bill for a customer with a home with 2,300 square feet is approximately $92.00.

Q: The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. The first observations in the sample for y and x were 300 and 18, respectively. Given this, the residual value for the first observation is approximately 81.6.

Q: Given a regression equation of = 16 + 2.3x we would expect that an increase in x of 2.0 would lead to an average increase of y of 4.6.

Q: The sign on the intercept coefficient in a simple regression model will always be the same as the sign on the correlation coefficient.

Q: If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.

Q: If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.

Q: In developing a simple linear regression model it is assumed that the distribution of error terms will be normally distributed for all levels of x.

Q: In a simple regression model, the slope coefficient represents the average change in the independent variable for a one-unit change in the dependent variable.

Q: When a pair of variables has a positive correlation, the slope in the regression equation will always be positive.

Q: When the correlation coefficient for the two variables was -0.23, it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

Q: If two variables are uncorrelated, the sample correlation coefficient will be r = 0.00.

Q: In conducting a hypothesis test on the correlation between a pair of variables, we assume that each variable is normally and independently distributed.

Q: The fact that teachers' salaries in Wisconsin are correlated with egg prices in Texas means that the two variables are spuriously correlated since a change in one variable could not cause the change in the other.

Q: If two variables are spuriously correlated, it means that the correlation coefficient between them is near zero.

Q: If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.

Q: Given a sample correlation r = -0.5 and a sample size of n = 30, the test statistic for testing whether the two variables are significantly correlated is approximately t = -3.055.

Q: State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: GPA HOURS 3.14 25 2.75 30 3.68 11 3.22 18 2.45 22 2.80 40 3.00 15 2.23 29 3.14 10 2.90 0 The test statistic for testing whether the two variables are significantly correlated is approximately z = 1.56.

Q: In a university statistics course a correlation of -0.8 was found between numbers of classes missed and course grade. This means that the fewer classes students missed, the higher the grade.

Q: Given a sample of size n = 15 and a sample correlation of r = 0.7, the value of the test statistic for conducting a hypothesis test of the correlation is t = 3.53.

Q: You are given the following sample data for two variables: Y X 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 Based upon these sample data, and testing at the 0.05 level of significance, the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

Q: You are given the following sample data for two variables: Y X 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 The sample correlation coefficient for these data is approximately r = 0.755.

Q: A bank is interested in determining whether its customers' checking balances are linearly related to their savings balances. A sample of n = 20 customers was selected and the correlation was calculated to be +0.40. If the bank is interested in testing to see whether there is a significant linear relationship between the two variables using a significance level of 0.05, the value of the test statistic is approximately t = 1.8516.

Q: In conducting a hypothesis test for a correlation, the correct probability distribution to use is the F distribution.

Q: A cellular phone service provider believes that there is negative correlation between the minutes used by its customers and the age of the customer. To test this, the following would be the appropriate null and alternative hypotheses: H0: ρ = 0.0 Ha: ρ ≠ 0.0

Q: A correlation coefficient computed from a sample of data values selected from a population is called a statistic and is subject to sampling error.

Q: If the correlation coefficient for two variables is computed to be a -0.70, the scatter plot will show the data to be downward sloping from left to right.

Q: A perfect correlation between two variables will always produce a correlation coefficient of +1.0

Q: Two variables have a correlation coefficient that is very close to zero. This means that there is no relationship between the two variables.

Q: A correlation of -0.9 indicates a weak linear relationship between the variables.

Q: A study was recently conducted by Major League Baseball to determine whether there is a correlation between attendance at games and the record of home team's opponent. In this study, the dependent variable would be the record of the home team's opponent.

Q: A research study has stated that the taxes paid by individuals is correlated at a .78 value with the age of the individual. Given this, the scatter plot would show points that would fall on straight line on a slope equal to .78.

Q: When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.

Q: If two variables are related in a positive linear manner, the scatter plot will show points on the x,y space that are generally moving from the lower left to the upper right.

Q: A scatter plot is useful for identifying a linear relationship between the independent and dependent variable, but it is not particularly useful if the relationship is curvilinear.

Q: In developing a scatter plot, the decision maker has the option of connecting the points or not.

Q: Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.

Q: When constructing a scatter plot, the dependent variable is placed on the vertical axis and the independent variable is placed on the horizontal axis.

Q: A dependent variable is the variable that we wish to predict or explain in a regression model.

Q: The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

Q: The scatter plot is a two dimensional graph that is used to graphically represent the relationship between two variables.

Q: In a contingency analysis, the greater the difference between the actual and the expected frequencies, the more likely: A) H0should be rejected. B) H0should be accepted. C) we cannot determine H0. D) the smaller the test statistic will be.

Q: We expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when: A) H0is false. B) H0is true. C) H0is falsely accepted. D) the variables are related to each other.

Q: What does the term expected cell frequencies refer to? A) The frequencies found in the population being examined B) The frequencies found in the sample being examined C) The frequencies computed from H0 D) the frequencies computed from H1

Q: What does the term observed cell frequencies refer to? A) The frequencies found in the population being examined B) The frequencies found in the sample being examined C) The frequencies computed from H0 D) The frequencies computed from H1

Q: To use contingency analysis for numerical data, which of the following is true? A) Contingency analysis cannot be used for numerical data. B) Numerical data must be broken up into specific categories. C) Contingency analysis can be used for numerical data only if both variables are numerical. D) Contingency analysis can be used for numerical data only if it is interval data.

Q: We are interested in determining whether the opinions of the individuals on gun control (as to Yes, No, and No Opinion) are uniformly distributed. A sample of 150 was taken and the following data were obtained. Do you support gun control Number of Responses Yes 40 No 60 No Opinion 50 The conclusion of the test with alpha = 0.05 is that the views of people on gun control are: A) uniformly distributed. B) not uniformly distributed. C) inconclusive. D) None of the above

Q: A chi-square test for goodness-of-fit is used to test whether or not there are any preferences among 3 brands of peas. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be: A) 20 B) 30 C) 60 D) 33

Q: A researcher is using a chi-square test to determine whether there are any preferences among 4 brands of orange juice. With alpha = 0.05 and n = 30, the critical region for the hypothesis test would have a boundary of: A) 7.81 B) 8.71 C) 8.17 D) 42.25

Q: Consider a goodness-of-fit test with a computed value of chi-square = 1.273 and a critical value = 13.388, the appropriate conclusion would be to: A) reject H0. B) fail to reject H0. C) take a larger sample. D) take a smaller sample.

Q: If a sample with n = 60 subjects distributed over 3 categories was selected, a chi-square test for goodness-of-fit will be used. How many degrees of freedom will be used in determining the chi-square test statistic? A) 1 B) 2 C) 16 D) 64

Q: In a goodness-of-fit test about a population distribution, if one or more parameters are left unspecified in H0, they must be estimated from the sample data. This will reduce the degrees of freedom by ________ for each estimated parameter. A) 1 B) 2 C) 3 D) None of the above

Q: In a chi-square goodness-of-fit test, by combining cells we guard against having an inflated test statistic that could have caused us to: A) incorrectly reject the H0. B) incorrectly accept the H0. C) incorrectly reject the H1. D) incorrectly accept the H1.

Q: A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Frequency Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100 Based on these data, conduct a goodness-of-fit test using a 0.10 level of significance. Which conclusion is correct? A) Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical value). B) Arrivals are uniformly distributed over the weekday because (test statistic) > (critical value). C) Arrivals are not uniformly distributed over the weekday because (test statistic) < (critical value). D) Arrives are uniformly distributed over the weekday because (test statistic) < (critical value).

Q: Which of the following statements is true in the context of a chi-square goodness-of-fit test? A) The degrees of freedom for determining the critical value will be the number of categories minus 1. B) The critical value will come from the standard normal table if the sample size exceeds 30. C) The null hypothesis will be rejected for a small value of the test statistic. D) A very large test statistic will result in the null not being rejected.

Q: The degrees of freedom for the chi-square goodness-of-fit test are equal to ________, where k is the number of categories. A) k + 1 B) k - 1 C) k + 2 D) k - 2

Q: If the null hypothesis is not rejected, you do not need to worry when the expected cell frequencies drop below 5.0

Q: If a contingency analysis test performed with a 4 6 design results in a test statistic value of 18.72, and if alpha = .05, the null hypothesis that the row and column variable are independent should be rejected.

Q: If a contingency analysis test is performed with a 4 6 design, and if alpha = .05, the critical value from the chi-square distribution is 24.9958

Q: In a contingency analysis the expected values are based on the assumption that the two variables are independent of each other.

Q: Unlike the case of goodness-of-fit testing, with contingency analysis there is no restriction on the minimum size for an expected cell frequency.

Q: In a chi-square contingency analysis application, the expected cell frequencies will be equal in all cells if the null hypothesis is true.

Q: In a chi-square contingency test, the number of degrees of freedom is equal to the number of cells minus 1.

Q: In a contingency analysis, we expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when H0is true.

Q: A contingency table and a cross-tabulation table are two separate things and should not be used for the same purpose.

Q: To employ contingency analysis, we set up a 2-dimensional table called a contingency table.

Q: Contingency analysis can be used when the level of data measurement is nominal or ordinal.

Q: A cell phone company wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers. Regularly use text messaging Do not regularly use text messaging Under 21 82 38 21-39 57 34 40 and over 6 83 To conduct a test of independence, the difference expected value for the "40 and over and regularly use text messaging" cell is just over 43 people.

Q: A study was recently done in the United States in which car owners were asked to indicate whether their most recent car purchase was a U.S. car, a German car, or a Japanese car. The people in the survey were divided by geographic region in the United States. The following data were recorded. US Japanese German East Coast 200 200 50 Central 250 100 20 West Coast 80 300 40 Given this situation, to test whether the car origin is independent of the geographical location of the buyer, the expected number of people in the sample who bought a German made car and who lived on the East Coast is just under 40 people.

Q: In order to apply the chi-square contingency methodology for quantitative variables, we must first break the quantitative variable down into discrete categories.

Q: A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed: radio television newspaper under 21 30 50 5 21-40 20 25 30 41 and over 30 30 50 Given this data, if we wish to test whether the preferred news source is independent of age, for an alpha = .05 level, the test statistic is computed to be approximately 40.70.

Q: In conducting a test of independence for a contingency table that has 4 rows and 3 columns, the number of degrees of freedom is 11.

Q: When the variables of interest are both categorical and the decision maker is interested in determining whether a relationship exists between the two, a statistical technique known as contingency analysis is useful.

Q: A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed: Males Females Have Laptop 120 70 No Laptop 50 60 Given this information, if an alpha level of .05 is used, the test statistic for determining whether having a laptop is independent of gender is approximately 14.23.

Q: Managers use contingency analysis to determine whether two categorical variables are independent of each other.

Q: Contingency analysis is used only for numerical data.

Q: Contingency analysis helps to make decisions when multiple proportions are involved.