Explanation:
To determine the confidence level that the newspaper used in their report, we need to use the margin of error and sample size to calculate the standard error and then use a standard normal distribution table to find the corresponding confidence level.
The formula for the margin of error is:
Margin of Error = Critical Value * Standard Error
Where the critical value depends on the level of confidence, and the standard error is the standard deviation of the sample mean, given by:
Standard Error = Standard Deviation / sqrt(Sample Size)
We can estimate the population standard deviation using the sample proportion, given by:
Standard Deviation = sqrt((p * (1-p)) / n)
where p is the proportion of individuals in the sample who are unemployed, which we can estimate using the sample proportion of unemployed individuals.
Since we don't have this information, we can use a conservative estimate of p = 0.5, which will give us the maximum possible standard deviation.
Therefore, the standard error can be estimated as:
Standard Error = sqrt((0.5 * (1-0.5)) / 4000) = 0.0125
Using the margin of error of 1%, we can solve for the critical value:
0.01 = Z * 0.0125
Z = 0.01 / 0.0125 = 0.8
Looking up the corresponding value in a standard normal distribution table, we find that the confidence level is approximately 77.5%.
Therefore, the newspaper most likely used a confidence level of 77.5% in their report.