Functions > Statistics > Probability Distributions > Example: T-Score of a Vector of Data
  
Example: T-Score of a Vector of Data
Compute a t-score for a vector of normally distributed data with respect to a specified mean.
1. Define a vector of data to analyze.
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2. Collect the sample statistics.
Number of samples
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Sample mean
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Sample standard deviation
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Standard error of the mean
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Degree of freedom
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3. Define the significance level and the proposed population mean.
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4. Calculate the t-score.
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5. State the null and the alternative hypothesis.
H0: m ≤ μ
H1: m > μ
6. Calculate the p-value and test the hypothesis.
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There is a 0.106 probability that the test statistic is greater than the one observed, assuming that the null hypothesis is true. The comparison between the p-value and the significance level indicates there is no evidence that the alternative hypothesis is true.
7. Calculate the limit of the critical region and test the hypothesis.
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Accept the null hypothesis. There is no evidence that the mean is greater than μ.
8. Plot the Student's t-distribution (blue), the boundary of the critical region (red), and the t-score (green).