Multiple Choice
Find the critical value, , for an 80% confidence interval.
7. Sampling Distributions & Confidence Intervals: Mean
Introduction to Confidence Intervals
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Which of the following is NOT a valid method for increasing the precision of a confidence interval?
A
Decreasing the confidence level
B
Using a more accurate measurement tool
C
Increasing the sample size
D
Increasing the variability in the data
Verified step by step guidance1
Step 1: Understand the concept of precision in a confidence interval. Precision refers to how narrow the confidence interval is. A narrower interval indicates higher precision, while a wider interval indicates lower precision.
Step 2: Analyze the impact of decreasing the confidence level. Lowering the confidence level reduces the range of the confidence interval, making it narrower and increasing precision. This is a valid method for increasing precision.
Step 3: Consider the use of a more accurate measurement tool. Using a tool that reduces measurement error decreases variability in the data, which in turn narrows the confidence interval and increases precision. This is also a valid method.
Step 4: Evaluate the effect of increasing the sample size. A larger sample size reduces the standard error, which narrows the confidence interval and increases precision. This is another valid method.
Step 5: Examine the impact of increasing variability in the data. Higher variability increases the standard error, which widens the confidence interval and decreases precision. Therefore, increasing variability is NOT a valid method for increasing the precision of a confidence interval.
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