Question

For a two-tailed test and a sample of 15 observations at a 10% significance level, the critical value of t is:

a) 1.761
b) 2.145
c) -2.145
d) -1.761

Answer 1

The critical value of t for a two-tailed test and a sample of 15 observations at a 10% significance level is approximately 2.145.

Step-by-step explanation:

The critical value of t for a two-tailed test and a sample of 15 observations at a 10% significance level can be found using the t-distribution table or a calculator. Given the sample size of 15, the degrees of freedom (df) are equal to n-1 which is 14. For a 10% significance level, we need to find the critical t-value with an area of 0.05 in both tails, which means 0.025 in each tail.

Referring to the t-distribution table or using a calculator function like invT, for a two-tailed test with 14 degrees of freedom and a 0.025 area in each tail, the critical value of t is approximately 2.145.