3) The table below shows results from a study in which some dental patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury. Use a 0.05 significance level to test for independence between the type of restoration and the presence of any adverse health conditions. Do amalgam restorations appear to affect health conditions? \begin{tabular}{|l|l|l|} \hline & \begin{tabular}{l} Amalga \\ m \end{tabular} & Composite \\ \hline \begin{tabular}{l} Adverse Health Condition \\ Reported \end{tabular} & 135 & 145 \\ \hline \begin{tabular}{l} No Adverse Health Condition \\ Reported \end{tabular} & 132 & 122 \\ \hline \end{tabular} 4) 1. Consider the following data values of variables \( x \) and \( y \). \begin{tabular}{c|cccccc} \( x \) & 2 & 4 & 6 & 8 & 10 & 13 \\ \hline\( y \) & 7 & 11 & 17 & 21 & 27 & 36 \end{tabular} a. Determine the least squares regression line (equation). b. Find the predicted value of \( y \) for \( x=9 \). C. What does the value of the slope of the regression line tell you? f. Calculate the Pearson coefficient of correlation. What sign does it have? Why?
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- Null hypothesis (\(H_0\)): The type of restoration and the presence of adverse health conditions are independent. - Alternative hypothesis (\(H_a\)): The type of restoration and the presence of adverse health conditions are not independent. Show more…
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Madhur L.
Suppose the least-squares equation ŷi = 2.25 + 0.64 xi is estimated and the coefficient of determination (R²) is calculated as 0.81. The sample correlation ( r ) will a. equal 0.9 b. equal -0.9 c. equal 0.8 d. cannot be determined from the information given 2. Which of the following may be used to determine whether there is significant causal relationship between the dependent variable and independent variable at 5% significance level? a. Testing at 5% significance level if the true slope coefficient ( β₂ ) is equal to zero. b. Checking to see if the 95% confidence interval of the true slope coefficient contains the value of β₂ = 0 c. Neither of the above. d. Both (a) and (b) are correct.
Question 6.2 A study was conducted to determine the effect of extra help sessions attended on student’s ability to avoid mistakes on a 20- multiple choice test. The data shown below represent the number of extra help sessions attended(x) and the average number of mistakes (y) recorded. x | 1 | 2 | 3 | 4 | 5 | 6 y | 6.1 | 5.1 | 5.0 | 4.2 | 3.7 | 3.2 ∑x_i = 21 ∑y_i = 27.3 ∑x_iy_i = 85.8 ∑x_i^2 = 91 ∑y_i^2 = 129.79 n = 6. a) Calculate the sample correlation coefficient. Describe the relationship between the number of extra help sessions attended and the average number of mistakes recorded. Calculate the sample correlation coefficient. b) Find the best fitting line relating the number of extra help sessions attended and the average number of mistakes recorded. c) Interpret the slope of this line in the context of the problem. d) What is the estimated number of mistakes recorded when the number of extra help sessions is 5. e) Circle your answer, either true or false, for each question. 1. Regression procedures are appropriate for studying a relationship between two categorical variables. True False 2. Correlation/association implies causation. True False 3. Correlation coefficients (correlations) range from -1 to 1. True False 4. If a correlation is close to 0, it means there is no relationship between X and Y. True False
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