Question

Suppose that we are testing H0: μ = μ0 versus H1: μ < μ0 with sample size of n = 25. Calculate bounds on the P -value for the following observed values of the test statistic (use however many decimal places presented in the look-up table. Answers are exact):

(h) upper bound upon t0 = -1.3.

THE ANSWER IS NOT 0.15 OR 0.05

Answer 1

The value of the test statistic = t = -1.3 ~ t_25-1 = t₂₄

The P-Value is .10297415 for this one tailed test.

Now the P-Value is the probability of getting a test statistic that is at least as extreme as the one representing the sample data, assuming that the null hypothesis is true. So, in this case, we want to find P(t < - 1.3) with degrees of freedom = n-1 = 24

i.e. P-Value - P(t₂₄ < - 1.3) = .10297415

Please see the shaded region, which is the required p-value :

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