6. In the hypothetical datafile titled "Method of Teaching", you'll find 3 variables. "Mark" (or score) is the Score each of 20 students earned on some quiz. Another variable included is Gender (male or female). And the other variable is "Method" (whether the student was taught using positive reinforcement ("being nice") or punishment ("electric shock")). Use these data to find out (A) if men's and women's scores/marks statistically differ on the quiz, (B) if either being nice or electric shock works significantly better than the other teaching method to improve scores, and (C) if there's a significant interaction between gender and teaching method used (i.e., find out if men's and women's learning differed depending on the teaching method used). Answer questions below related to A through C. In your analysis, include descriptive statistics, an appropriate descriptive plot with Error Bars (representing 95% confidence intervals), and estimates of effect sizes for each of the three possible effects (A through C above). Interpret the effect sizes and use the plot/graph to interpret whether there is an interaction and describe what it means based on the graph. The appropriate statistical analysis to conduct to test our 3 research hypotheses is ___________. A) Repeated Measures ANOVA B) Pearson Correlation Coefficient C) Factorial ANOVA D) One-way ANOVA E) Partial Correlation F) Dependent Means t-test G) Independent Means t-test H) Chi-squared test of independence I) Spearman Correlation Coefficient or Kendall's tau-b Correlation
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Step 1: Conduct independent t-tests to compare the mean scores of men and women on the quiz. Show more…
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Title: Analysis of Student Performance in Different Discussion Sections of an Introductory Statistics Class Professor Echo teaches a large introductory statistics class (197 students) with eight discussion sections. He would like to test if student performance differs by discussion section, where each discussion section has a different teaching assistant. The summary table below shows the average final exam score for each discussion section, as well as the standard deviation of scores and the number of students in each section: Section Average Score Standard Deviation Number of Students Sec 2 92.94 4.21 33 Sec 3 91.11 5.58 19 Sec 4 91.8 3.43 10 Sec 5 92.45 5.92 29 Sec 6 89.3 9.32 33 Sec 7 88.3 7.27 10 Sec 8 90.12 6.93 32 Sec 9 93.45 4.57 31 The ANOVA output below can be used to test for differences between the scores from the different discussion sections: Source of Variation Df Sum Sq Mean Sq F value Pr(F) Section 7 525.01 75.00 1.87 0.0767 Residuals 189 7584.11 40.13 Conduct a hypothesis test to determine if these data provide convincing evidence that the average score varies across some (or all) groups. Check conditions and describe in your own words the steps you must take to proceed with the test. Hypotheses: Ho: μ1 = μ2 = μ8 Ha: At least one pair of means is different (b) Assume that the conditions required for this inference test are satisfied. What is the test statistic associated with this ANOVA test? (please round to two decimal places) (c) What is the p-value associated with this ANOVA test? (please round to four decimal places) (d) Interpret the conclusion of the test in the context of the study: Since the p-value is less than 0.05, there is enough evidence to claim a difference across the different sections in average scores.
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Two groups of students (males and females) were examined in Statistics for Decision Making course. The following were the scores obtained by the males and females samples consisting of ten students each: Group A (Males): 60, 44, 43, 77, 80, 98, 68, 67, 60, 48 Group B (Females): 12, 55, 80, 68, 75, 50, 32, 90, 56, 42 i. For each group, calculate the mean score and interpret your result. (3 marks) ii. Which group had varied scores? (4 marks) Traditionally, the demand for Kakabo Local Rice is determined by a number of factors. An economist has collected data on few of these factors and has estimated their contribution to the purchase behavior of customers. The tables below indicate the regression output of the quantity of 5kg bag of Kakabo Local Rice. Use the information in the tables to answer the questions that follow: Regression Statistics Multiple R: 0.9965 R Square Adjusted R Square Standard Error: 0.5332 Observations: 21 ANOVA Df SS MS F Significance F Regression 4 653.761 163.440 574.928 0.000 Residual 16 4.548 0.284 Total 20 658.310 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 9.104 7.352 1.238 0.233 -6.481 24.689 Price 0.137 -2.239 0.040 -0.599 -0.016 Income 0.267 0.127 0.051 -0.001 0.535 Taste 0.636 2.357 0.032 0.064 1.208 Population -0.050 -0.223 -0.527 0.427 i. State and explain the estimated equation for the 5kg bag of rice. (4 marks) ii. What percentage of the variation is not explained by the exogenous (independent) variables? (1 mark) iii. Which of the independent variable(s) is/are significant in explaining the changes in quantity of rice and why? (2 marks) iv. If price changes by 1 unit, state the range of values within which quantity will fall for 95% confidence level. (1 mark)
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Use the data in CARD for this exercise. (i) The equation we estimated in Example 15.4 can be written as $$\log (w a g e)=\beta_{0}+\beta_{1} e d u c+\beta_{2} e x p e r+\ldots+u$$ where the other explanatory variables are listed in Table $15.1 .$ In order for IV to be consistent, the IV for educ, nearc4, must be uncorrelated with $u$ . Could nearc4 be correlated with things in the error term, such as unobserved ability? Explain. (ii) For a subsample of the men in the data set, an IQ score is available. Regress $I Q$ on nearc4 to check whether average IQ scores vary by whether the man grew up near a four-year college. What do you conclude? (iii) Now, regress 1$Q$ on nearc4, smsa66, and the 1966 regional dummy variables $r e g 662, \ldots, r e g 669$ Are $I Q$ and $n e a r c 4$ related after the geographic dummy variables have been partialled out? Reconcile this with your findings from part (ii). (iv) From parts (ii) and (iii), what do you conclude about the importance of controlling for smsa66 and the 1966 regional dummies in the log(wage) equation?
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