Weights were measured from college students in September and later in April of t
ID: 3241924 • Letter: W
Question
Weights were measured from college students in September and later in April of their freshman year. The measurements are listed in the popup table below. Assume that we plan to use the sign test to test the claim of no difference between September weights and April weights. What requirements must be satisfied for this test? Is there any requirement that the populations must have a normal distribution or any other specific distribution? In what sense is this sign test a "distribution-free" test?
September weights 67 53 64 74 67 70 55 74 62 57
April Weights 66 52 68 77 67 71 60 82 65 58
What requirements must be satisfied for this test?
A.
There must be more than 30 matched pairs that approximately follow a normal distribution.
B.
The matched pairs must constitute a simple random sample.
C.
There must be more than 30 matched pairs.
D.
There must be more than 30 matched pairs that all constitute a simple random sample.
E.
The matched pairs must constitute a simple random sample that approximately follow a normal distribution.
F.
The matched pairs must approximately follow a normal distribution.
G.
There must be more than 30 matched pairs that all constitute a simple random sample and approximately follow a normal distribution.
H.
None of the above choices are correct.
Is there any requirement that the populations must have a normal distribution or any other specific distribution?
A.
The populations must have a Student t distribution.
B.
The populations must have an F distribution.
C.
The populations must have a normal distribution.
D.
The populations may have any distribution.
In what sense is this sign test a "distribution-free" test?
A.
The sign test is "distribution-free" in the sense that the Central Limit Theorem applies to it.
B.
The sign test is "distribution-free" in the sense that it does not require a normal distribution or any other specific distribution.
C.
The sign test is "distribution-free" in the sense that there is no distribution to the population.
D.
The sign test is "distribution-free" in the sense that researchers can use any distribution to find critical values and P-values.
Explanation / Answer
Answer:
Weights were measured from college students in September and later in April of their freshman year. The measurements are listed in the popup table below. Assume that we plan to use the sign test to test the claim of no difference between September weights and April weights. What requirements must be satisfied for this test? Is there any requirement that the populations must have a normal distribution or any other specific distribution? In what sense is this sign test a "distribution-free" test?
September weights 67 53 64 74 67 70 55 74 62 57
April Weights 66 52 68 77 67 71 60 82 65 58
What requirements must be satisfied for this test?
A.There must be more than 30 matched pairs that approximately follow a normal distribution.
Answer: B.The matched pairs must constitute a simple random sample.
C.There must be more than 30 matched pairs.
D.There must be more than 30 matched pairs that all constitute a simple random sample.
E.The matched pairs must constitute a simple random sample that approximately follow a normal distribution.
F.The matched pairs must approximately follow a normal distribution.
G.There must be more than 30 matched pairs that all constitute a simple random sample and approximately follow a normal distribution.
H.None of the above choices are correct.
Is there any requirement that the populations must have a normal distribution or any other specific distribution?
A.The populations must have a Student t distribution.
B.The populations must have an F distribution.
C.The populations must have a normal distribution.
Answer: D.The populations may have any distribution.
In what sense is this sign test a "distribution-free" test?
A.The sign test is "distribution-free" in the sense that the Central Limit Theorem applies to it.
Answer: B.The sign test is "distribution-free" in the sense that it does not require a normal distribution or any other specific distribution.
C.The sign test is "distribution-free" in the sense that there is no distribution to the population.
D.The sign test is "distribution-free" in the sense that researchers can use any distribution to find critical values and P-values.
Note: The Sign test is a non–parametric (distribution free) test, so we do not assume that the data is normally distributed. The test assumes independence, meaning that the paired observations are randomly and independently drawn.
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