Matilda has constructed three confidence intervals, all from

quiquenobi2v6

quiquenobi2v6

Answered question

2021-12-12

Matilda has constructed three confidence intervals, all from the same random sample. The confidence levels are 95%, 98%, 99.9%. The confidence intervals are
6.4<u<12.3, 5.1<u<13.6 and 6.8<u<11.8 Unfortunately, Matilda has forgotten which confidence interval goes with level. Match each confidence interval with its level.
What confidence goes with each the confidence level and indicate whether these confidence intervals are for a population mean or for a population proportion, also include support with the results.

Answer & Explanation

Donald Cheek

Donald Cheek

Beginner2021-12-13Added 41 answers

The widths of the given confidence interval: 
For 6.4<μ<12.3 width =12.36.4 =5.9 
For 5.1<μ<13.6 width =12.65.1 =8.5 
For 6.8<μ<11.8 width =11.86.8 =5 

The width of the confidence interval 5.1<μ<13.6 is the highest. Its corresponding confidence level would be 99.9% (highest among the given confidence levels). 
The width of the confidence interval 6.4<μ<12.3 is the second highest. Its corresponding confidence level would be 98% (second highest among the given confidence levels). 
The width of the confidence interval 6.8<μ<11.8 is the lowest. Its corresponding confidence level would be 95% (lowest among the given confidence levels). 
The range for the boundaries of confidence intervals for proportions is 0 to 1. The provided confidence intervals exceed 1. Due to the limitations being outside of 0 and 1, these confidence intervals are for a population mean. Additionally, the interval contains the number  μ , which represents the population mean.

Neil Dismukes

Neil Dismukes

Beginner2021-12-14Added 37 answers

Step 1
The given CI are for population mean because proportions are always less than 1.
Wider the CI, higher the value of confidence level.
12.36.4=5.9
13.65.1=8.5
11.96.8=5.1
Hence, (6.8, 11.9) is for 95%
(6.4, 12.3) is for 98% Cl
and (5.1, 13.6) is fro 99.9% Cl

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