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Assume the blood pressures of 10 people were measured before and after sleeping for the night. What is the corresponding critical t-value for a one-tailed, paired-samples t test with an alpha level of 0. 05 (5%). Please report your answer as an absolute value and include three decimal places.

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Using a t-distribution table or a t-critical value calculator, the critical value for a one- tailed t - test for the sample given at 0.05 α-level would be 1.833

The critical value for a one-tailed, paired sample t test can be defined thus :

  • [tex]t_{critical} = t_{α, df-1} [/tex]

  • Sample size, n = 10

The degree of freedom , df for a 1 - tailed t-test is calculated using the relation :

  • df = n - 1

Hence,

Degree of freedom, df = n - 1 = 10 - 1 = 9

Using a Tcritical value calculator or a t - distribution table :

[tex]t_{critical} = t_{0.05, 9} = 1.833 [/tex]

Therefore, the critical value for a one - tailed test at 0 05 level of confidence would be 1.833.

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