In a survey of 2035 adults in a certain country conducted during a period of economic uncertainty, $62 \%$ thought that wages paid to workers in industry were too low. The margin of error was 6 percentage points with $90 \%$ confidence. For parts (a) through (d) below, which represent a reasonable interpretation of the survey results? For those that are not reasonable, explain the flaw. (c) We are $90 \%$ confident that the interval from 0.56 to 0.68 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 suggests that this interval sets the standard for all the other intervals, which is not true. c. The interpretation is flawed. The interpretation indicates that the level of confidence is varying. D. The interpretation is flawed. The interpretation provides no interval about the population proportion.

Step 1 ：The question is asking whether the interpretation of the survey results is reasonable. The interpretation states that we are 90% confident that the interval from 0.56 to 0.68 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.

Step 2 ：This interpretation seems to be based on the given margin of error of 6 percentage points. Given that 62% of the surveyed adults thought that wages were too low, a margin of error of 6 percentage points would indeed result in a confidence interval from 0.56 (62% - 6%) to 0.68 (62% + 6%).

Step 3 ：However, to confirm this, we can calculate the confidence interval using the formula for the confidence interval of a proportion, which is \(p̂ ± Z*√((p̂(1-p̂))/n)\), where \(p̂\) is the sample proportion, \(Z\) is the Z-score corresponding to the desired confidence level, and \(n\) is the sample size.

Step 4 ：In this case, \(p̂ = 0.62\), \(Z = 1.645\) (corresponding to a 90% confidence level), and \(n = 2035\). Let's calculate the confidence interval.

Step 5 ：The calculated confidence interval is from approximately 0.60 to 0.64. This is slightly different from the given interval in the interpretation, which is from 0.56 to 0.68. Therefore, the interpretation is not entirely accurate. However, it is important to note that the calculated confidence interval is based on the assumption of a normal distribution and the approximation may not be exact.

Step 6 ：Final Answer: The interpretation is flawed. The interpretation provides an interval about the population proportion that is not entirely accurate based on the given margin of error and confidence level. The correct confidence interval, based on the given data, is approximately from 0.60 to 0.64. Therefore, the answer is \(\boxed{\text{(D) The interpretation is flawed. The interpretation provides no interval about the population proportion.}}\)