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.