Copyright © KAYLIN 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH NOVEMBER, 2024
STAT 203 Final Exam Questions and
Answers 100% Pass
What is SE? - ANSWER✔✔-Standard Error of p̂ = sqrt((p̂ (1-p̂ ))/n)
What is a confidence interval? - ANSWER✔✔-range of values in which a specified probability of the
means of repeated samples would be expected to fall
Property the population proportion p - ANSWER✔✔-p is fixed and does not vary. Rather the confidence
intervals as what's varying because of sampling variability.
What is z*? - ANSWER✔✔-This is the critical value z-score such that the upper tail area under the
standard normal curve equals to 100%-confidence level/ 2.
What is a confidence level? - ANSWER✔✔-the probability(percentages) that a confidence interval
encloses the population proportion p. Could be 90%, 95%, and 99%.
The higher the confidence level_______ - ANSWER✔✔-the larger the value of z*
What is ME? - ANSWER✔✔-Margin of error - balancing between certainty and precision.
ME = z*(SE)(p̂ )
What happens if we allow a larger margin of error? - ANSWER✔✔-the confidence interval will be wider
and hence will have a greater chance of including the true value of p. However, with a higher confidence
in capturing p, the interval becomes less precise (wider).
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, Copyright © KAYLIN 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH NOVEMBER, 2024
What are the assumptions and conditions for constructing a confidence interval? - ANSWER✔✔-- the
sample is randomly drawn from the population
- the sample values are independent (sample size is a small fraction of the population size)
- the sample size is sufficiently large (p is unknown, so we check the conditions: np̂ >/= 10 and n(1-p̂ ) >/=
10
What are the properties of a confidence interval? - ANSWER✔✔-centered at the sample proportion p̂
the width of a CI increases with the confidence level, and hence lower precision
the width of the CI decreases with the sample size hence greater precision (when the sample size is
doubled, the standard error decreases by a factor of sort(2)
How can we interpret a confidence interval for p? - ANSWER✔✔-- Over the collection of all confidence
intervals of a fixed confidence level C that could be constructed from repeated random samples of size n
obtained from the population, the percentage of confidence intervals that contain the true proportion p
equals to C
- We are C% confidence that the true proportion falls within the confidence interval that one has
obtained.
What are CI's constructed for? - ANSWER✔✔-For parameters not statistics (p not p̂ )
Why do we need to determine an appropriate sample size n? - ANSWER✔✔-with the intention of
estimating a population proportion, we need to achieve a certain precision in the estimate of the
population parameter. We need to specify the maximum tolerable margin of error and the confidence
level to find the required sample size.
Copyright ©Stuvia International BV 2010-2024 Page 2/8
STAT 203 Final Exam Questions and
Answers 100% Pass
What is SE? - ANSWER✔✔-Standard Error of p̂ = sqrt((p̂ (1-p̂ ))/n)
What is a confidence interval? - ANSWER✔✔-range of values in which a specified probability of the
means of repeated samples would be expected to fall
Property the population proportion p - ANSWER✔✔-p is fixed and does not vary. Rather the confidence
intervals as what's varying because of sampling variability.
What is z*? - ANSWER✔✔-This is the critical value z-score such that the upper tail area under the
standard normal curve equals to 100%-confidence level/ 2.
What is a confidence level? - ANSWER✔✔-the probability(percentages) that a confidence interval
encloses the population proportion p. Could be 90%, 95%, and 99%.
The higher the confidence level_______ - ANSWER✔✔-the larger the value of z*
What is ME? - ANSWER✔✔-Margin of error - balancing between certainty and precision.
ME = z*(SE)(p̂ )
What happens if we allow a larger margin of error? - ANSWER✔✔-the confidence interval will be wider
and hence will have a greater chance of including the true value of p. However, with a higher confidence
in capturing p, the interval becomes less precise (wider).
Copyright ©Stuvia International BV 2010-2024 Page 1/8
, Copyright © KAYLIN 2024/2025 ACADEMIC YEAR. ALL RIGHTS RESERVED FIRST PUBLISH NOVEMBER, 2024
What are the assumptions and conditions for constructing a confidence interval? - ANSWER✔✔-- the
sample is randomly drawn from the population
- the sample values are independent (sample size is a small fraction of the population size)
- the sample size is sufficiently large (p is unknown, so we check the conditions: np̂ >/= 10 and n(1-p̂ ) >/=
10
What are the properties of a confidence interval? - ANSWER✔✔-centered at the sample proportion p̂
the width of a CI increases with the confidence level, and hence lower precision
the width of the CI decreases with the sample size hence greater precision (when the sample size is
doubled, the standard error decreases by a factor of sort(2)
How can we interpret a confidence interval for p? - ANSWER✔✔-- Over the collection of all confidence
intervals of a fixed confidence level C that could be constructed from repeated random samples of size n
obtained from the population, the percentage of confidence intervals that contain the true proportion p
equals to C
- We are C% confidence that the true proportion falls within the confidence interval that one has
obtained.
What are CI's constructed for? - ANSWER✔✔-For parameters not statistics (p not p̂ )
Why do we need to determine an appropriate sample size n? - ANSWER✔✔-with the intention of
estimating a population proportion, we need to achieve a certain precision in the estimate of the
population parameter. We need to specify the maximum tolerable margin of error and the confidence
level to find the required sample size.
Copyright ©Stuvia International BV 2010-2024 Page 2/8
