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. state the null hypothesis. choose the correct answer below. a. ( h_0 ): the average height of the mountain ash trees in the sample is 250 feet, the same as the average height of typical old growth douglas fir. b. ( h_0 ): the average height of all mountain ash trees in southeast australia is 250 feet, the same as the average height of typical old growth douglas fir. c. ( h_0 ): the average height of all mountain ash trees in southeast australia is 293 feet. d. ( h_0 ): the average height of all mountain ash trees in southeast australia is more than 250 feet, which is the average height of typical old growth douglas fir. e. ( h_0 ): the average height of the mountain ash trees in the sample is 293 feet.

Explanation:

The null hypothesis ($H_0$) is a statement of no difference or equality. In hypothesis testing about population means, the null hypothesis is about the population parameter (not the sample statistic). Here, we are comparing the population mean height of Mountain Ash trees in southeast Australia to the known average height of Douglas - Firs (250 feet).

Answer:

B. $H_0$: The average height of all Mountain Ash trees in southeast Australia is 250 feet, the same as the average height of typical old growth Douglas Fir.