Question

A two-sided test of a hypothesis, based on a sample of size 9, yields a P-value

of .035. Which of the following best describes the possible range of t values
that yields this P-value?
OA. 1.83 OB. 2.45 < t < 2.90
OC. 1.89 OD. 1.11 OE. 1.86 < t < 2.31

Answer 1

Let's go step-by-step:

We are given:

- A two-tailed test

- Sample size n = 9

- P-value = 0.035

For a two-tailed test, a P-value of 0.035 means that 2.5% of the t-distribution lies in each tail. Since this is a two-tailed test, the total critical region is 5% (2.5% in each tail).

With a sample size of 9, the t-distribution has 9-1 = 8 degrees of freedom.

So we need to find the t-values that correspond to the 2.5th and 97.5th percentiles of the t-distribution with 8 degrees of freedom.

Looking at a t-distribution table or using a calculator, we find:

2.5th percentile t-value = 1.86

97.5th percentile t-value = 2.31

Therefore, the range of possible t values yielding a P-value of 0.035 is:

1.86 < t < 2.31

The answer is E: 1.86 < t < 2.31 b