Statistics Quiz on Hypothesis Testing
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Questions and Answers

What type of test is used when comparing means of a single continuous variable?

  • Regression
  • Single mean T-test (correct)
  • Related sample T-test
  • Chi-square test

    • Which test is appropriate for two unrelated continuous variables?

  • Correlation test
  • Chi-square test
  • Single mean T-test
  • Unrelated sample T-test (correct)

    • When measuring the association between two continuous variables, which of the following tests is suitable?

  • Single mean T-test
  • Regression (correct)
  • Chi-square test
  • Related sample T-test

    • Which of the following tests is specifically used for categorical variables?

    <p>Chi-square test</p> Signup and view all the answers

    In which situation would a related sample T-test be applied?

    <p>Examining means before and after an intervention</p> Signup and view all the answers

    What type of test would you use for comparing means of a single group over time?

    <p>Related sample T-test</p> Signup and view all the answers

    Which type of variable is needed for a correlation test?

    <p>Continuous variables</p> Signup and view all the answers

    When would you choose an unrelated sample T-test?

    <p>Comparing means from two different groups</p> Signup and view all the answers

    What types of tests can a student's t-test be classified as?

    <p>One-tail and two-tail</p> Signup and view all the answers

    What must be identified first when conducting a t-test?

    <p>The level of significance</p> Signup and view all the answers

    If the level of significance is 0.05, which t-value should be used for 3 degrees of freedom in a two-tail test?

    <p>3.182</p> Signup and view all the answers

    Which of the following t-values corresponds to a 0.995 level of significance with 5 degrees of freedom?

    <p>9.925</p> Signup and view all the answers

    Which value indicates a higher confidence level in a t-test?

    <p>0.001</p> Signup and view all the answers

    What does a one-tail t-test evaluate?

    <p>Differences in only one direction</p> Signup and view all the answers

    Which of the following t-values is NOT associated with a one-tail test at a 0.9 significance level for 2 degrees of freedom?

    <p>3.747</p> Signup and view all the answers

    How many degrees of freedom are indicated for the t-value of 4.032 at a significance level of 0.99?

    <p>4</p> Signup and view all the answers

    What is the correct value of t score for α=0.05 and DF=4 in a two-tail test?

    <p>2.776</p> Signup and view all the answers

    In correlation analysis, which hypothesis represents the null hypothesis (Ho)?

    <p>ρ = 0</p> Signup and view all the answers

    Which number represents the critical t value for a one-tail test at α=0.05 with 6 customers surveyed?

    <p>2.976</p> Signup and view all the answers

    What is the formula used to calculate the test statistic in correlation analysis?

    <p>t = r / sqrt(1 - r^2)</p> Signup and view all the answers

    When performing a two-tailed test, which value should you enter to find your t critical value?

    <p>1 - α/2</p> Signup and view all the answers

    What is the value of the test statistic (t) when the correlation coefficient (r) equals 0.91?

    <p>4.39</p> Signup and view all the answers

    What indicates that there is strong evidence against the null hypothesis in hypothesis testing?

    <p>t &gt; tcritic</p> Signup and view all the answers

    For DF = n - 2 with n = 6, what is the value of DF?

    <p>4</p> Signup and view all the answers

    What is the primary purpose of using multiple regression analysis in the context of Pizza Hut's research?

    <p>To establish a hypothesis about customer satisfaction</p> Signup and view all the answers

    In the regression equation provided, what does 'Y' represent?

    <p>The dependent variable</p> Signup and view all the answers

    Which of the following options represents the independent variables in Pizza Hut's multiple regression analysis?

    <p>Location and service</p> Signup and view all the answers

    What do the coefficients (β1...n) represent in the regression equation?

    <p>The effect of independent variables on the dependent variable</p> Signup and view all the answers

    In the given context, which hypothesis suggests that some independent variables significantly affect customer satisfaction?

    <p>Ho: Some variables affect satisfaction</p> Signup and view all the answers

    Which component of the regression equation accounts for unexplained variability?

    <p>Error term (ε)</p> Signup and view all the answers

    Which regression type includes more than one independent variable?

    <p>Multiple linear regression</p> Signup and view all the answers

    What is the meaning of βo in the regression equation?

    <p>Intercept of the regression line</p> Signup and view all the answers

    Which of the following must be established to claim causation between two variables?

    <p>Both A and C</p> Signup and view all the answers

    What does a correlation coefficient (r) primarily indicate?

    <p>The strength and direction of an association between two variables</p> Signup and view all the answers

    Which of the following best describes extraneous variables in the context of causation?

    <p>Uncontrolled factors that can affect the relationship between IV and DV</p> Signup and view all the answers

    What additional knowledge is necessary for establishing causation beyond statistical analysis?

    <p>Underlying knowledge and theories about the variables</p> Signup and view all the answers

    In regression analysis, what is the primary focus when analyzing data?

    <p>Investigating the nature and degree of association between variables</p> Signup and view all the answers

    What must a researcher do to ensure that their analysis supports a claim of causation?

    <p>Account for and eliminate potential confounders</p> Signup and view all the answers

    Which condition is NOT a requirement for establishing causation?

    <p>The sample size must exceed a certain threshold</p> Signup and view all the answers

    What does regression analysis help to measure among variables?

    <p>Nature and degree of association</p> Signup and view all the answers

    What does dummy-variable coding involve when categorizing variables?

    <p>Coding the category of interest as 1 and others as 0</p> Signup and view all the answers

    In a dummy-variable coding system with n categories, how many categories are coded?

    <p>n-1 categories</p> Signup and view all the answers

    Which of the following categories would be considered the baseline in a binary case of gender coding?

    <p>Female, coded as 0</p> Signup and view all the answers

    In the multinomial case, which consumer type is coded as 1 in dummy-variable coding?

    <p>Light user</p> Signup and view all the answers

    When is the variable that is not coded in dummy-variable coding defined as the baseline?

    <p>In both binary and multinomial cases</p> Signup and view all the answers

    What is the main purpose of simple regression analysis in Marketing Research?

    <p>To analyze the relationship between two variables</p> Signup and view all the answers

    What specific relationship was Pizza Hut investigating through hypothesis testing?

    <p>The effect of customer satisfaction on likelihood to recommend</p> Signup and view all the answers

    In the coding for consumer types, how is a heavy user represented?

    <p>Coded as 0 in all dummies</p> Signup and view all the answers

    Study Notes

    Marketing Research - Correlation & Regression Analysis

    • Correlation Analysis: Measures the strength of the relationship between two variables. It doesn't imply causation.
    • Pearson Correlation Coefficient (r): Measures the degree of linear association between two continuous variables (X and Y). Values range from -1 to +1. A value of 0 indicates no linear association.
    • Scatter Plots: Visual representations of the relationship between two variables. They show the degree and direction of the correlation.
    • Correlation Effect Sizes:
      • Weak: ±0.1
      • Moderate: ±0.3
      • Strong: ±0.5

    Correlation Analysis Example

    • Pizza Hut and Customer Satisfaction: Pizza Hut wants to measure if customer satisfaction is related to the likelihood of customers recommending the company.
    • Hypothesis:
      • Null Hypothesis (H0): There is no correlation between customer satisfaction and recommendation.
      • Alternative Hypothesis (H₁): There is a positive correlation between customer satisfaction and recommendation.
    • Variables:
      • Independent Variable (IV): Customer satisfaction
      • Dependent Variable (DV): Likelihood to recommend
    • Correlation Coefficient: A correlation coefficient of 0.91 indicates a strong positive correlation between customer satisfaction and likelihood to recommend.

    Conditions for Causation

    • Association: A correlation must exist between the independent and dependent variables.
    • Time Precedence: The independent variable must occur before the dependent variable.
    • Elimination of Confounders: Need to eliminate extraneous variables that could influence the relationship between the IV and DV.

    Regression Analysis

    • Statistical Technique: Regerssion analysis relates two or more variables to create a model that relates one or more independent variables to the dependent variable.
    • Variables:
      • Independent Variables (IVs): Potential factors affecting the dependent variable.
      • Dependent Variable (DV): The variable you want to predict or explain.
    • Analysis type: (Linear, Multiple).
    • Coding Categorical Variables (Dummy Variables): Categorical variables are coded numerically as 1 or 0 for each category/property respectively to allow analysis.

    Simple Linear Regression

    • Equation: Y = β₀ + β₁X₁ + ε.
    • Interpreting Parameters:
      • β₀: The intercept. The mean value of Y when X = 0.
      • β₁: The coefficient of the independent variable. The change in Y for every 1-unit change in X.
      • ε: The error term. Unexplained variation in Y.

    Multiple Linear Regression

    • Equation: Y = β₀ + β₁X₁ + β₂X₂ + ... + βₙXₙ + ε.
    • Interpreting Parameters: Same as simple linear regression, but multiple IVs.

    Regression Analysis: Significance Testing

    • Assess the significance of the relationship between variables using a p-value less than a chosen alpha level (example 0.05).

    Chapter Overview

    • Nature and Scope: Understanding marketing research, perspectives and implementation, in contexts like decision making
    • Data Collection: Exploratory (secondary, qualitative/observational), Descriptive (survey research), and Causal (experimentation, sampling and statistics).
      • Detailed steps on Data and analysis from Chapters 5-19.

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    Related Documents

    Marketing Research - Correlation & Regression Analysis PDF

    Description

    Test your knowledge on various statistical tests used for analyzing data in hypothesis testing. This quiz covers tests for continuous variables, categorical variables, and more, providing a comprehensive overview of when to use each test. Ideal for students and professionals wanting to solidify their understanding of statistical methodologies.

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