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. based on this t - statistic, what is the conclusion? choose the correct answer below. a. there is not sufficient evidence to indicate that the average height of all mountain ash trees in southeast australia is more than 250 feet. b. there is sufficient evidence to indicate that the average height of all mountain ash trees in southeast australia is equal to 250 feet. c. there is sufficient evidence to indicate that the average height of the mountain ash trees in this sample is more than 250 feet. d. there is sufficient evidence to indicate that the average height of all mountain ash trees in southeast australia is more than 250 feet. e. there is not sufficient evidence to indicate that the average height of the mountain ash trees in this sample is more than 250 feet.

Explanation:

Step1: Analyze the purpose of the test

The goal is to test if the average height of all Mountain Ash trees (population) is more than 250 feet. The sample is used to make inferences about the population.

Step2: Consider the t - statistic value

A large t - statistic (6.661 in this case) indicates that the sample mean (293 feet) is far from the hypothesized population mean (250 feet) in terms of standard errors.

Step3: Evaluate each option

• Option A: Incorrect. A large t - statistic provides evidence.
• Option B: Incorrect. The test is for "more than" 250, not "equal to".
• Option C: Incorrect. The test is about the population mean, not just the sample mean.
• Option D: Correct. The t - statistic suggests that the sample provides sufficient evidence to infer about the population mean being more than 250.
• Option E: Incorrect. The t - statistic shows evidence.

Answer:

D. There is sufficient evidence to indicate that the average height of all Mountain Ash trees in southeast Australia is more than 250 feet