Question

You have an SRS of size 15 and calculate the one-sample t statistic. What is the critical value t* such that

(a) t has probability 0.01 to the right of t*?

(b) t has probability 0.85 to the left of t*?

Answer 1

Given that sample size ( n ) = 15

Degrees of freedom ( df ) = n - 1 = 15 - 1 = 14

We want to find, one sample t test critical value t^* for following cases:

a) t has a probability 0.01 to the right of t^*

Therefore, in this case significance level = 0.01

t-critical value at 0.05 level of significance with df = 14 is,

t^* = 2.624

b) t has probability 0.85 to the left of t^*

Therefore, in this case significance level = 1 - 0.85 = 0.15

t-critical value at 0.15 level of significance with df = 14 is,

t^* = 1.076