Questions: (c) We are 90% confident that the interval from 0.52 to 0.64 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low. Is the interpretation reasonable? A. The interpretation is reasonable. B. The interpretation is flawed. The interpretation indicates that the level of confidence is varying. C. The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true. D. The interpretation is flawed. The interpretation provides no interval about the population proportion.

(c) We are 90% confident that the interval from 0.52 to 0.64 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low.

Is the interpretation reasonable?
A. The interpretation is reasonable.
B. The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
C. The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.
D. The interpretation is flawed. The interpretation provides no interval about the population proportion.

Transcript text: (c) We are $90 \%$ confident that the interval from 0.52 to 0.64 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low. Is the interpretation reasonable? A. The interpretation is reasonable. B. The interpretation is flawed. The interpretation indicates that the level of confidence is varying. C. The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true. D. The interpretation is flawed. The interpretation provides no interval about the population proportion. Video Get more help - Clear all

Solution

Solution Steps

Step 1: Define the Confidence Interval and Level

We are given a confidence interval of $ (0.52, 0.64) $ and a confidence level of $ 90\% $. This means we are $ 90\% $ confident that the true proportion of adults who believe wages paid to workers in industry are too low lies within this interval.

Step 2: Interpret the Confidence Interval

The interpretation of a confidence interval is that if we were to take many samples and construct a confidence interval from each sample, approximately $ 90\% $ of those intervals would contain the true population proportion. Therefore, the statement that we are $ 90\% $ confident that the true proportion lies within $ (0.52, 0.64) $ is a valid interpretation.

Step 3: Analyze the Options

We analyze the provided options regarding the interpretation:

Option A states that the interpretation is reasonable.
Option B suggests that the interpretation indicates a varying confidence level, which is incorrect.
Option C claims that the interval sets a standard for all other intervals, which is also incorrect.
Option D states that the interpretation provides no interval about the population proportion, which is false since the interval is explicitly given.

Given the analysis, the only correct interpretation is that the statement is reasonable.