Confidence intervals - fill in the gaps - Numbas at mathcentre.ac.uk

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Mario Orsi

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Mario Orsi

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Rabail Tahir 2 years, 1 month ago

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Question statement

Fill in the gaps in the following sentences regarding confidence intervals.

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A confidence interval represents a range of values within which we are likely (but not certain) to find a Unnamed gapparameter.

Hint: input one of "categorical", "population", "sample".

Advice

Revise confidence intervals, e.g., Sections 5.2 and 7.1 of OpenIntro Statistics (4th edition).

a) A CI aims at providing a "guess" (in the form of an interval) for a population (note that we don't need to guess a sample mean, we know exactly what it is, whereas we normally don't know a population mean, and that's why we need to guess).

b) A CI for the population mean ( $\mu$ ) is built around the best available estimate for $\mu$ , which is the sample mean.

c) The most common/conventional CI is the $95\%$ CI (which also corresponds to the most common significance level $\alpha=5\%$ ).

d) As a CI is defined as either $\pm z^*\times SE$ or $\pm t^*\times SE$ , the larger SE the larger the CI.

e) Considering d) above, and noting that $SE$ is defined as either $\sqrt{\frac{p(1-p)}{n}}$ (for a proportion) or $\frac{SD}{\sqrt{n}}$ (for numerical data), a larger sample size $n$ will result in a smaller CI.

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This question is used in the following exams:

Izabela's copy of Confidence Intervals by Izabela Walczak in Statistics 2020.
Scientific Practice exam Jan 2021 by Mario Orsi in Stats.
Mathematics for Data Science Class Test 1 by Rabail Tahir in Rabail's workspace.
PARTNERS: Confidence Intervals by Chris Graham in PARTNERS: Maths and Physics, Newcastle University.
Mathematics in Data Science Class test 1 by Rabail Tahir in Rabail's workspace.
Test 5 by Mario Orsi in BiomedSkills.
Resit MDS summer_2024 by Rabail Tahir in Rabail's workspace.
ResitExam20Qs by Mario Orsi in Stats.

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Confidence intervals - fill in the gaps

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Rabail Tahir 2 years, 1 month ago

Mario Orsi 4 years, 9 months ago

Mario Orsi 4 years, 9 months ago

Mario Orsi 4 years, 9 months ago

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