A dental research team investigating a new tooth filling material conducted a test comparing a new hardening method to the current method used by a majority of dentists. The study randomly assigned its subjects to be treated with either the new method or the current method, and measured the index of hardness for each subject after treatment. For the 62 subjects treated with the new method, the mean hardness index was 7.71 with a standard deviation of 0.73. For the 66 subjects treated with the current method, the mean hardness index was 7.48 with a standard deviation of 0.51. The standard error (SE) of the difference between the sample means is 0.112. a) Would you consider the difference in sample means to be practically significant? Why or why not? Briefly discuss the difference between statistical significance and practical significance in your response. b) Is there sufficient evidence, at the 5% significance level, to conclude that the mean index of hardness (for all patients) with the new hardening method is significantly higher than with the current method? Show your work. Conduct a complete analysis and state the conclusion in the context of the researcher’s study. c) Based on your conclusion, what type of error (Type 1 or Type 2) is possible? Why? Explain what that type of error would mean in the context of this study
A dental research team investigating a new tooth filling material conducted a test comparing a new hardening method to the current method used by a majority of dentists. The study randomly assigned its subjects to be treated with either the new method or the current method, and measured the index of hardness for each subject after treatment. For the 62 subjects treated with the new method, the mean hardness index was 7.71 with a standard deviation of 0.73. For the 66 subjects treated with the current method, the mean hardness index was 7.48 with a standard deviation of 0.51. The standard error (SE) of the difference between the sample means is 0.112.
a) Would you consider the difference in sample means to be practically significant? Why or why not? Briefly discuss the difference between statistical significance and practical significance in your response.
b) Is there sufficient evidence, at the 5% significance level, to conclude that the mean index of hardness (for all patients) with the new hardening method is significantly higher than with the current method? Show your work. Conduct a complete analysis and state the conclusion in the context of the researcher’s study.
c) Based on your conclusion, what type of error (Type 1 or Type 2) is possible? Why? Explain what that type of error would mean in the context of this study
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