Question

Identify -

• Null & alternative hypothesis

• Test statistic

• P-value

• Conclusion about null hypothesis

• Layman’s final conclusion that addresses the original claim

Dora recently 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 costal 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 the sample mean = 293 ft. and the sample standard deviation = 25 ft. Assume the heights of the 15 trees in Dora’s sample are representative of the heights of all Mountain Ash trees in southeast Australia.

Answer 1

Here the null hypothesis is .

The alternative hypothesis is .

Here sample size n = 15, sample mean = 293 and sample standard deviation s = 25.

Here the tests statistic is .

Putting the values we get the value of the test statistic t = 6.66153136.

Here the P-value of the test is P[T > 6.66153136] where T follows (n-1) = 14 degrees of freedom.

So, the P-value of this test is 0.00000538 [Using R code pt(6.66153136,14,lower.tail = F)].

As the P-value is less than 0.01, we can reject the null hypothesis at 1% level of significance.

So, she can conclude that at 1% level of significance Eucalyptus regnans or Mountain Ash trees are taller than the costal Douglas Firs of her native state of Oregon in the United States.