You are studying the difference in body mass measured in grams for Gentoo penguins where the penguins are caught and measured early in the season and the same penguins are caught and measured again late in the season. Here are some data and summary statistics. Please perform a paired t-test for these data.
[
egin{array}{|c|c|c|c|}
hline
ext{Penguin} & ext{Early} & ext{Late} & ext{Diff} \
hline
1 & 4950 & 4950 & 0 \
2 & 4300 & 4297 & -3 \
3 & 4350 & 4353 & 3 \
4 & 4450 & 4451 & 1 \
5 & 4500 & 4506 & 6 \
6 & 4750 & 4754 & 4 \
7 & 4300 & 4301 & 1 \
8 & 4625 & 4628 & 3 \
ext{mean} & 4528.13 & 4530.00 & 1.88 \
ext{sd} & 232.78 & 233.32 & 2.75 \
hline
end{array}
]
Please write your response with labels corresponding to each portion of the question. Also, be sure to show your work where applicable.
A. (2 points) Write out your hypotheses H0 and H1
B. Choose alpha = 0.05
C. (8 points) Write out the 4 assumptions of a t-test (4 pts) and whether each assumption is met in this case (4 pts). Please assume that normality is met
D. (10 points) Perform the test to calculate t
E. (5 points) Find the t-table value.
F. (5 points) Write your statistical conclusion
G. (5 points) Write a conclusion that the public would understand
You are studying the difference in body mass measured in grams for Gentoo penguins where the penguins are caught and measured early in the season and the same penguins are caught and measured again late in the season. Here are some data and summary statistics. Please perform a paired t-test for these data.
[
egin{array}{|c|c|c|c|}
hline
ext{Penguin} & ext{Early} & ext{Late} & ext{Diff} \
hline
1 & 4950 & 4950 & 0 \
2 & 4300 & 4297 & -3 \
3 & 4350 & 4353 & 3 \
4 & 4450 & 4451 & 1 \
5 & 4500 & 4506 & 6 \
6 & 4750 & 4754 & 4 \
7 & 4300 & 4301 & 1 \
8 & 4625 & 4628 & 3 \
ext{mean} & 4528.13 & 4530.00 & 1.88 \
ext{sd} & 232.78 & 233.32 & 2.75 \
hline
end{array}
]
Please write your response with labels corresponding to each portion of the question. Also, be sure to show your work where applicable.
A. (2 points) Write out your hypotheses H0 and H1
B. Choose alpha = 0.05
C. (8 points) Write out the 4 assumptions of a t-test (4 pts) and whether each assumption is met in this case (4 pts). Please assume that normality is met
D. (10 points) Perform the test to calculate t
E. (5 points) Find the t-table value.
F. (5 points) Write your statistical conclusion
G. (5 points) Write a conclusion that the public would understand