Q&A Hero

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: 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 correlation between these two variables is approximately -.461

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: GPAHOURS3.14252.75303.68113.22182.45222.80403.00152.23293.14102.900If the university wished to test the claim that the correlation between hours worked and GPA is negative, the following null and alternative hypotheses would be appropriate:

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: 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 In this study the independent variable is the number of hours worked off campus per week.

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:

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 .05, the correct null and alternative hypotheses to test are:H0 : r = 0.0Ha : r 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: A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below. Hispanic Non-Hispanic Seat belts worn 31 148 Seat belts not worn 283 330 Referring to these data, which of the following conclusions should be reached if the appropriate hypothesis is conducted using an alpha = .05 level? A) The mean value for Hispanics is the same as for Non-Hispanics. B) There is no relationship between whether someone is Hispanic and whether they wear a seat belt. C) The use of seat belts and whether a person is Hispanic or not is statistically related. D) None of the above

Q: A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below. Hispanic Non-Hispanic Seat belts worn 31 148 Seat belts not worn 283 330 Referring to these data, the calculated test statistic is: A) approximately -0.9991 B) nearly -0.1368 C) about 48.1849 D) approximately 72.8063

Q: A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below. Hispanic Non-Hispanic Seat belts worn 31 148 Seat belts not worn 283 330 Referring to these data, which test would be used to properly analyze the data in this experiment? A) x2 test for independence in a two-way contingency table B) x2 test for equal proportions in a one-way table C) ANOVA F-test for interaction in a 2 2 factorial design D) x2 goodness-of-fit test

Q: In testing a hypothesis that two categorical variables are independent using the x2 test, the expected cell frequencies are based on assuming: A) the null hypothesis. B) the alternative hypothesis. C) the normal distribution. D) the variable are related.

Q: When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom. A) 5 B) 6 C) 7 D) 12

Q: For a chi-square test involving a contingency table, suppose H0 is rejected. We conclude that the two variables are: A) curvilinear. B) linear. C) related. D) not related.

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 contingency analysis, the value of the test statistic is: A) 9.2104 B) 88.3 C) 275.02 D) 14.6

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 contingency analysis using a 0.01 level of significance, the value of the critical value is: A) 15.0863 B) 5.9915 C) 9.2104 D) 11.0705

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 contingency analysis, the number of degrees of freedom is: A) 6 B) 5 C) 3 D) 2

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 Based on the data above what is the expected value for the "under 21 and regularly use text messaging" cell? A) 82 B) 50 C) 120 D) 58

Q: How can the degrees of freedom be found in a contingency table with cross-classified data? A) When df are equal to rows minus columns B) When df are equal to rows multiplied by columns C) When df are equal to rows minus 1 multiplied by columns minus 1 D) Total number of cell minus 1

Q: In performing chi-square contingency analysis, to overcome a small expected cell frequency problem, we: A) combine the categories of the row and/or column variables. B) increase the sample size. C) Both A and B D) None of the above

Q: In a chi-square contingency analysis, when expected cell frequencies drop below 5, the calculated chi-square value tends to be inflated and may inflate the true probability of ________ beyond the stated significance level. A) committing a Type I error B) committing a Type II error C) Both A and B D) All of the above

Q: In a contingency analysis, the greater the difference between the actual and the expected frequencies, the more likely: A) H0 should be rejected. B) H0 should 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) H0 is false. B) H0 is true. C) H0 is 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: 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 What is the value of the test statistic needed to conduct a goodness-of-fit test? A) 8.75 B) 7.7794 C) 2.46 D) 2.50

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 To conduct a goodness-of-fit test, what is the expected value for Friday? A) 20 B) 25 C) 16 D) 100

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 Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is: A) 9.4877 B) 11.0705 C) 7.7794 D) 9.2363

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 this information how many degrees for freedom are involved in this goodness of fit test? A) 99 B) 100 C) 4 D) 5

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 H0 is 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.