Question

The t statistic for a test of

?0:?=41

??:?≠41
based on n = 6 observations has the value t = -1.1.

(a) What are the degrees of freedom for this statistic?

(b) Using the appropriate table in your formula packet, bound the p-value as closely as possible:
___ < p-value < ___

Answer 1

This is the two tailed test .

(a)

The degrees of freedom = 6 - 1 = 5

(b)

P-value = 2 * P(t ₅ < -1.1) = 0.3215

0.25 < p-value < 0.50

or

P-value > 0.10

Answer 2

(a) The degrees of freedom for this statistic can be calculated using the formula:

df = n - 1 = 6 - 1 = 5

So the degrees of freedom are 5.

(b) To find the p-value, we need to use a t-distribution table with 5 degrees of freedom. Since the t-value (-1.1) is negative, we need to find the area to the left of -1.1 in the t-distribution table.

Using a t-distribution table with 5 degrees of freedom, we find that the area to the left of -1.1 is approximately 0.168. Since this is a two-tailed test, we need to double this value to get the total area in both tails:

2 * 0.168 = 0.336

Therefore, the p-value is bounded as follows:

0.336 < p-value < 1