Basic Business Statistics, Student Value Edition
14th Edition
ISBN: 9780134685113
Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat
Publisher: PEARSON
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Chapter 11, Problem 34PS
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Explain the concept of interaction in a two-factor factorial design.
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The interaction effect in a factorial design is considered, because it may modify the main effects of the independent variables.
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Chapter 11 Solutions
Basic Business Statistics, Student Value Edition
Ch. 11 - An experiment has a single factor with five groups...Ch. 11 - You are working with the same experiment as in...Ch. 11 - You are working with the same experiment as in...Ch. 11 - Consider an experiment with three groups, with...Ch. 11 - Prob. 5PSCh. 11 - You are working the same experiment as in Problem...Ch. 11 - One of the steps involved in the processing of...Ch. 11 - The more costly and time-consuming it is to export...Ch. 11 - A hospital conducted a study of the waiting time...Ch. 11 - A manufacturer of pens has hired an advertising...
Ch. 11 - Prob. 11PSCh. 11 - Brand valuations are critical to CEOs, financial...Ch. 11 - A pet food company has a business objective of...Ch. 11 - A transportation strategist wanted to compare the...Ch. 11 - Consider a two-factor factorial design with three...Ch. 11 - Prob. 16PSCh. 11 - Prob. 17PSCh. 11 - Prob. 18PSCh. 11 - Given a two-way ANOVA with two levels for factor A...Ch. 11 - Given a two-factor factorial experiment and the...Ch. 11 - Given the results from Problem 11.20, a. at the...Ch. 11 - An experiment was conducted to study the extrusion...Ch. 11 - Prob. 23PSCh. 11 - Prob. 24PSCh. 11 - A glass manufacturing company wanted to...Ch. 11 - Prob. 26PSCh. 11 - Prob. 27PSCh. 11 - Prob. 28PSCh. 11 - Prob. 29PSCh. 11 - Prob. 30PSCh. 11 - Prob. 31PSCh. 11 - Prob. 32PSCh. 11 - Prob. 33PSCh. 11 - Prob. 34PSCh. 11 - Prob. 35PSCh. 11 - Prob. 36PSCh. 11 - Prob. 37PSCh. 11 - Prob. 38PSCh. 11 - Suppose that, when setting up the experiment in...Ch. 11 - A hotel wanted to develop a new system for...Ch. 11 - Refer to the room service experiment in Problem...Ch. 11 - Prob. 42PS
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- Can higher-order interactions be dropped to error in the analysis of fractional factorial designs? Why or why not ?arrow_forwardA researcher wants to examine the effect of humidity on amount of hair frizz. How could the researcher address this question using a multiple-groups design? What are the pros and cons of this design choice? What is/are the appropriate analysis/analyses? How could the researcher address this question using a dependent multiple-groups design? What are the pros and cons of this design choice? Address whatever design you select or consider both types of dependent multiple-groups designs. What is/are the appropriate analysis/analyses?arrow_forwardA two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication. In this two-factor study, factor A is medication versus no medication and factor B is male versus female. The medicine is expected to reduce blood pressure for both males and females, but it is expected to have a much greater effect for males. What pattern of results should be obtained if the medication works as predicted? A significant main effect for factor A (medication) A significant interaction A significant main effect for factor A and a significant interaction An insignificant main effect for factor A (medication)arrow_forward
- In a two factor factorial design with two design factors A and B, why do we generally include the interaction term in the model? What is the major concern if the model ignores the interaction effect?arrow_forwardA researcher wants to see if gender and / or income affects the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affects the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. Below is the data set followed by the results:arrow_forwardA study was conducted to assess the influence of various factors on the start of new firms in the computer chip industry. For a sample of 70 countries the following model was estimated: ŷ = -59.31 + 4.983x1 + 2.198x2 + 3.816x3 – 0.310x4 (1.156) (0.210) (2.063) (0.330) -0.886x5 + 3.215x6 + 0.85x7 (3.055) (1.568) (0.354) R2 = 0.766 where ŷ = new business starts in the industry X1 = population in millions X2 = industry size x3 = measure of economic quality of life measure of political quality of life measure of environmental quality of life measure of health and educational quality of life X4 X5 X6 = x7 = measure of social quality of life The numbers in parentheses under the coefficients are the estimated coefficient standard errors. (a) Determine which coefficients in the model are statistically significant? Provide a justification for your answer. (b) Is the overall regression equation statistically significant at the 1% level? Justify your answer.arrow_forward
- 2. How do you identify which variable in a study is the factor? How do you identify the levels of a factor? How do you identify the dependent variable?arrow_forwardA researcher wants to see if gender and/or income affect the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affect the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. What do the results of this study mean to you?arrow_forwardA researcher wants to see if gender and/or income affect the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affect the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. What is the null hypothesis?arrow_forward
- A researcher wants to see if gender and/or income affect the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affect the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. Is there significance for either gender or income?arrow_forwardA researcher wants to see if gender and/or income affect the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affect the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. What is one research hypothesis (there are three possible hypotheses here – name them all if you can.arrow_forwardA researcher wants to see if gender and/or income affect the total amount of help given to a stranger who is sitting on the side of a busy road with a sign asking for help. The independent variables are gender, income, and the interaction of gender and income. The dependent variable is total help. He wants to know if one or both factors – or the interaction of the two - affect the total amount of help offered. Because he is analyzing two independent variables (gender and income), he used a factorial ANOVA. His results show the main effect of each of the independent variables on the dependent variable (total help) and the interaction effect. The researcher is using a 95% confidence interval which means that he wants to be at least 95% sure that his independent variables affected total help if he rejects the null hypothesis. what is the significance of the interaction of gender and income?arrow_forward
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