Find the critical values and rejection regions for the indicated t-test, level of significance a, and sample size n. Left-tailed test, a = 0.10, n = 11

t -critical is -1.37

Step-by-step explanation:

Solution:-

- There are two parameters to determine the critical values of t-test.

                  Degree of freedom = n - 1

- Where, n = sample size

And,

                  Significance Level α = denotes the probability of the the t distribution above or below the vritical value.

- The type of test:

                Left tail : The leftmost region is defined by the significance level

                 Right tail : The right most region is defined by the significance level

                 Two tail : Both tails ( left and right ) are defined by the significance level

- The given data has the following:

                  α = 0.1  , n = 11

                  degree of freedom df = n - 1 = 11 - 1 = 10

                  Type : left tailed

- The t-critical value is defined by as follows:

                   P ( X < t-critical ) = α

                   P ( X < t-critical ) =  0.1

- Use the t-look up table and determine the corresponding value:

                   P ( X < -1.37 ) =  0.1

Hence, t -critical is -1.37.

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step-by-step explanation: