Question

In: Statistics and Probability

Environmentalists who were worried about the presence of barnacles along the Pacific Coast wanted to see...

Environmentalists who were worried about the presence of barnacles along the Pacific Coast wanted to see whether Oregon had more barnacles than California. They randomly selected 7 locations in California and 6 locations in Oregon. Working at the edge of the water in each location, they put down frames that covered 0.25 square meters and counted the barnacles inside the frame. Their results are summarized in the table below.

Group

State

# of Locations

(n)

Sample Mean Number of Barnacles

(x)

Sample Standard Deviation

(s)

Oregon

26.9

1.49

California

11.9

2.90

a. (2 points) What degrees of freedom would you use in the two-sample hypothesis test to compare Oregon and California? Why?

b. What is the test statistic for comparing the mean densities of barnacles in Oregon and California? Show your work.

c. The environmental scientists who conducted this study published a report which concluded that “the average number of barnacles per 0.25 m2 was statistically significantly higher in Oregon than in California, with α = 0.001.” Do your results agree with their published report?

Solutions

Expert Solution

(a)

The degrees of freedom would you use in the two-sample hypothesis test to compare Oregon and California = n1 + n2 - 2 = 6 + 7- 2 = 11 ,

since it an independent samples t test with degrees of frredom for Sample 1 = 6 and degrees of frredom for Sample 2 = 7.

(b)

Pooled Standard Deviation (sP) is given by:

the test statistic for comparing the mean densities of barnacles in Oregon and California is given by:

(c)

= 0.001

df = 11

One Tail - Right Side Test

From Table,critical value of t = 4.025

Since the claculated value of t 11.397 is greater than critical value of t = 4.025, the difference is significant. Reject null hypothesis.

So,

Answer is:

Our results agree with their published report that “the average number of barnacles per 0.25 m2 was statistically significantly higher in Oregon than in California, with α = 0.001".

orchestra answered 1 year ago

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