Explore the fundamentals of sampling distribution through diverse scenarios in this quiz. Assess your understanding of how sample sizes influence distribution shapes, means, and variability, crucial for statistical accuracy and decision-making.
μ = 42%
μ = 2.5%
μ = 0.42%
μ = 58%
μ = 1.2%
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Normal model may be used to describe distribution of sample proportions. Randomization condition is satisfied: the students were selected at random and are therefore representative of all students at the college 10% condition is satisfied: the 100 students are less than 10% of all students at the college Success/failure condition is satisfed: np = 10 and nq = 90 are both greater than 10.
Normal model may not be used to describe distribution of sample proportions. Randomization condition is not satisfied: the students were selected at random but only from those students leaving the student union building, not from the whole student body. Those leaving the student union building may not be representative of all students at the college - those suffering from depression are more likely to stay in their rooms and may not be out as much, participating in activities at the student union building.
Normal model may not be used to describe distribution of sample proportions. Success/failure condition is not satisfed: np = 10 and nq = 90 are both greater than 10.
Normal model may not be used to describe distribution of sample proportions. Distribution of population is not normal
Normal model may not be used to describe distribution of sample proportions. 10% condition is not satisfied: the 100 students are less than 10% of all students at the college
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σ = 2.74%
σ = 6.38%
σ = 5.48%
σ = 2.52%
σ = 5.05%
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No, Normal model may not be used: 10% condition is not satisfied since the 12 women in the sample represent less than 10% of women in the city
No, Normal model may not be used: Independence assumption is not satisfied: since the women in the sample may live in the same neighborhood, the chance of picking a woman with a high income depends on who has already been selected.
Yes, Normal model may be used. Randomization condition: The women were selected at random Independence assumption: It is reasonable to think that incomes of randomly selected women are mutually independent. Large enough sample condition: a sample of 12 is large enough for the Central Limit Theorem to apply 10% condition is satisfied since the 12 women in the sample certainly represent less than 10% of women in the city
No, Normal model may not be used: Large enough sample condition is not satisfied: since the distribution of incomes in the original population is skewed, a sample of 12 is not large enough
No, Normal model may not be used since incomes of women in the city are not normally distributed but are skewed to the right
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I and III only
II only
II and III only
III only
I only
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Normal, center at μ, standard deviation sqrt(σ/n)
Skewed right, center at μ, standard deviation sqrt(σ/n)
Skewed right, center at μ, standard deviation σ/sqrt(n)
Normal, center at μ, standard deviation σ/sqrt(n)
There is not enough information to describe the sampling distribution model.
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III only
I and III only
II only
I only
II and III only
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0.6517
0.3483
0.6966
0.7803
0.2197
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0.5879
0.0132
0.9868
0.4121
0.9614
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