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STA 2023 Exam 2 Questions and Complete Solutions Graded A+.
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STA 2023 Exam 2 Questions and Complete Solutions Graded A+.
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STA 2023 Exam 2Questions and Complete
Solutions Graded A+
p̂ - Answer: the sample proportion
p̂ = x/n (#successes/total # in sample)
What are the assumptions of that must hold for the sampling distribution of the sample proportion to
be normally distributed? - Answer: np≥15 *AND* n(1-p)≥15
If our assumptions are met, what is the mean of the sampling distribution of the sample proportion? -
Answer: p (the population mean)
T/F: The sample proportion and sample mean are random variables. - Answer: True.
How can you distinguish question about the sampling distribution of the sample proportion from a
question about the sampling distribution of the sample mean? - Answer: will often include the word
"proportion," a percentage, and a deal with with categorical values
If you know you are dealing with a sampling distribution question and you see that the standard
deviation is given, what can you assume? - Answer: You can assume that you are dealing with a question
about the sampling distribution of the sample mean and *NOT* the sampling distribution of the sample
proportion.
Describe the sampling distribution of the sample proportion, assuming np≥15 and n(1-p)≥15. - Answer:
p̂ ~N(p, √(p(1-p)/n))
, T/F: If np≤15 and n(1-p)≤15, you can add 2 successes and 2 failures to the approximate sampling
distribution for the sample proportion. - Answer: *FALSE.* This "trick" *ONLY* works with confidence
intervals. If np≤15 and n(1-p)≤15, you cannot work with the sampling distribution of the sample
proportion because you cannot assume that it is normal.
x̄ - Answer: The sample mean, which is the average of the observations in our sample.
What are the assumptions that must hold true for the sampling distribution of the sample mean to be
normally distributed? - Answer: n≥30 or the original population was normally distributed
If the sampling distribution of the sample mean is normally distributed, what is its mean? - Answer: The
population mean (μ)
Describe the sampling distribution of the sample mean, assuming n≥30 or the original population was
normally distributed. - Answer: x̄ ~N(μ, σ/√n)
Central Limit Theorem - Answer: Even when the population's probability distribution is not bell shaped,
the sampling distribution of the sample mean is bell-shaped when the same size is large enough (n≥30).
Population Distribution - Answer: The distribution for the overall population, which is based on
parameters such as the population mean and the population standard deviation.
Data Distribution - Answer: The distribution of the data we collect in practice. We collect samples in
order to create a data distribution so that we can estimate the population. The larger the sample size,
the more the better the data distribution approximates the population distribution.
The data distribution looks more like the population distribution when the sample size is (low/high). -
Answer: high
Sample means tend to cluster more around the population mean when the sample size is (low/high). -
Answer: high
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