95% Confidence Level
Definition
A 95% confidence level means that if we were to repeat our sampling process multiple times, approximately 95% of the resulting confidence intervals would contain the true population parameter. It represents a high level of confidence in the estimate.
Analogy
Imagine you have a bag of 100 marbles, and you want to estimate the proportion of red marbles. You randomly select 20 marbles, calculate the confidence interval for the proportion, and repeat this process multiple times. Around 95 out of 100 intervals will contain the true proportion within them.
Related terms
Significance Level: The probability threshold used to determine if results are statistically significant or due to chance.
Confidence Level vs. Confidence Interval: The confidence level is the probability associated with capturing the true parameter, while a confidence interval is an estimation range.
Sampling Distribution: A theoretical distribution that represents all possible sample values and their probabilities for a given statistic.
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Practice Questions (4)
A student constructed a confidence interval for the difference in proportions and found (-0.02, 0.08). What can they conclude at the 95% confidence level?
A researcher constructs a confidence interval for the difference in proportions and finds (0.12, 0.28). What is the correct interpretation of this interval at the 95% confidence level?
A researcher constructs a confidence interval for the difference in proportions and finds (-0.01, 0.09). What can be concluded at the 95% confidence level?
A researcher constructs a confidence interval for the difference in proportions and finds (-0.08, 0.02). What can be concluded at the 95% confidence level?
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