Question

dora likes to explore. recently, she explored southeast australia where she found some very large trees known as eucalyptus regnans or mountain ash. she wondered if they were taller, on average, than the coastal douglas firs of her native state of oregon in the united states, which have an average height of 250 feet in old growth areas. dora measured the heights of 15 mountain ash trees in southeast australia and found an average height of these trees of 293 feet. suppose ( s = 25 ) feet. assume the heights of the 15 trees in doras sample are representative of the heights of all mountain ash trees in southeast australia. the t - statistic for this problem is 6.661. how many degrees of freedom does this t - statistic have?
choose the correct answer below.
○ a. 14
○ b. 15
○ c. 13
○ d. 24
○ e. the t - statistic does not have degrees of freedom.

Explanation:

Step1: Recall the formula for degrees of freedom in a one - sample t - test

The formula for degrees of freedom ($df$) in a one - sample t - test is $df=n - 1$, where $n$ is the sample size.

Step2: Identify the sample size

In this problem, the sample size $n = 15$ (the number of Mountain Ash trees measured).

Step3: Calculate the degrees of freedom

Using the formula $df=n - 1$, substitute $n = 15$ into the formula: $df=15 - 1$.
$$df = 14$$

Answer:

A. 14