Problem 3: After teaching marine science, biology, and environmental science maj

Question

Problem 3: After teaching marine science, biology, and environmental science majors also the fact that I live in California, I become real interested in the crabs in Baltimore, MD. Baltimore is known for their blue crabs, so I went out in a big boat and caught three types of crabs; the Atlantic Ghost Crab (Ocypode quadrata), the Blue Crab (Callinectes sapidus), and the Fiddler Crab (Libinia emarginata). My good friend Jamear told me that I should expect a 2:4:8 ratio between these crabs in the bay (Which Bay?). I caught 560 crabs of these types of crabs. I caught 85 Atlantic Ghost Crabs, 155 Blue Crabs, and 320 Fiddler Crabs. I want the probability of me telling Jamear he is wrong to be 0.05 when he is right.

What is the population? What is my sample and sample size?

What does 2:4:8 mean?

What distribution would you use to model this problem?

What type of statistical test will we use?

Hypothesis Testing Frame

State statistical question

State the H0 and H1 using words.

State Level of Significance & Make a decision rule

Make a decision about H0 based on data

State the conclusion

Problem 4: Jamear decides to go out and catch 441 more crabs. He finds 347 Atlantic Ghost Crabs, 48 Blue Crabs, and 46 Fiddler Crabs. Use a significance level at 0.1 and 0.01 and compare the results.

Hypothesis Testing Frame

State statistical question

State the H0 and H1 using words.

State Level of Significance & Make a decision rule

Make a decision about H0 based on data

State the conclusion

Explanation / Answer

Problem 3:

Population: All three types of crabs in Baltimore

Sample : He  caught 560 crabs of these types of crabs

Sample size n = 560

Ratio 2:4:8 means these ratio follows Atlantic Ghost Crabs :Blue Crabs : Fiddler Crabs

Are these values commensurate with the general crabs count which is in the ratio of 2:4:8 for various crabs respectively?

H0: The given data commensurate with the general crabs count is in the ratio 2:4: 8

H1: The given data commensurate with the general crabs count is in the not ratio 2:4: 8

From the given data, the expected frequencies are calculated as Ei = Oi*ratio/14

Num Categories: 3
Degrees of freedom: 2

Test Statistic, X^2: 0.4687
Critical X^2: 5.991471
P-Value: 0.7911

Here P-value > alpha 0.05, we accept H0

Thus we conclude that the given data(crabs) follows in the ration 2:4:8

Problem 4:

Population: All three types of crabs

Sample : He  caught 441 crabs of these types of crabs

Sample size n = 441

Ratio 2:4:8 means these ratio follows Atlantic Ghost Crabs :Blue Crabs : Fiddler Crabs

Are these values commensurate with the general crabs count which is in the ratio of 2:4:8 for various crabs respectively?

H0: The given data commensurate with the general crabs count is in the ratio 2:4: 8

H1: The given data commensurate with the general crabs count is in the not ratio 2:4: 8

From the given data, the expected frequencies are calculated as Ei = Oi*ratio/14

Num Categories: 3
Degrees of freedom: 2

Test Statistic, X^2: 1496.9365

Critical X^2: 9.210334 at alpha = 1%
P-Value: 0.0000

Here P-value < alpha 0.05, we do not accept H0

Thus we conclude that the given data(crabs) not follows in the ration 2:4:8

Again

Critical X^2: 4.605166 at alpha = 10%
P-Value: 0.0000

Here P-value < alpha 0.05, we do not accept H0

Thus we conclude that the given data(crabs) not follows in the ration 2:4:8

Oi Ei (Oi-Ei)^2/Ei Atlantic Ghost 85 80 0.3125 Blue 155 160 0.15625 Fiddler 320 320 0 Total: 560 0.46875

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