If The Absolute Value Of Your Calculated Statistic Exceeds

1if The Absolute Value Of Your Calculatedt Statistic Exceeds The Crit

1. If the absolute value of your calculated t-statistic exceeds the critical value from the standard normal distribution, you can (Points : 1) [removed] [removed] [removed] [removed]

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The statement emphasizes a fundamental principle in hypothesis testing, particularly in the context of comparing a calculated t-statistic to a critical value derived from the standard normal distribution or a t-distribution. When conducting a statistical test, researchers formulate a null hypothesis and an alternative hypothesis, then compute a test statistic based on sample data. The critical value serves as a threshold that determines whether the null hypothesis should be rejected or not, based on the level of significance (α).

In hypothesis testing, the t-statistic is used to assess whether the sample data provides sufficient evidence to reject the null hypothesis. The absolute value of this t-statistic is compared to the critical value, which depends on the chosen significance level, the degrees of freedom, and the distribution used (t-distribution or normal distribution). If the absolute value of the calculated t-statistic surpasses the critical value, it indicates that the observed data is statistically significant, and the null hypothesis can be rejected at the specified level of significance.

Specifically, when the absolute value of the t-statistic exceeds the critical value, it suggests that the observed difference or relationship in the sample data is unlikely under the null hypothesis. This leads to conclusions supporting the alternative hypothesis, implying that the effect or association observed is statistically meaningful. Conversely, if the t-statistic does not exceed the critical value, the evidence is insufficient to reject the null hypothesis, and it remains a plausible explanation for the data.

The importance of this comparison lies in controlling the Type I error rate, which is the probability of incorrectly rejecting a true null hypothesis. By setting a significance level (commonly 0.05), researchers determine the critical value that corresponds to the desired confidence level. The decision rule—comparing the absolute value of the t-statistic to this critical value—is a straightforward and effective method for making inferential decisions based on sample data.

In summary, the key point conveyed by the statement is that surpassing the critical value with the absolute t-statistic signifies statistical significance, leading to the rejection of the null hypothesis. This process underpins many statistical analyses across various fields, including social sciences, healthcare, business, and engineering, facilitating informed decision-making from empirical data.

References

  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the Behavioral Sciences. Cengage Learning.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
  • Chatterjee, S., & Hadi, A. S. (2012). Regression Analysis by Example. John Wiley & Sons.
  • Upton, G., & Cook, I. (2014). Understanding Statistics. Oxford University Press.
  • McClave, J. T., & Sincich, T. (2017). A First Course in Statistics. Pearson.
  • Newbold, P., Carlson, W., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
  • Larson, R., & Farber, M. (2014). Elementary Statistics: Picturing the World. Pearson.
  • Rumsey, D. J. (2012). Statistics for Dummies. Wiley.
  • Wilkinson, L., et al. (2014). The Grammar of Graphics (2nd ed.). Springer.

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