Following is a sample of unemployment rates in percentage po

Following is a sample of unemployment rates (in percentage points) in the United States sampled from the period 1990 – 2004. { 4.2, 4.7, 5.4, 5.8, 4.9)

Assuming the distribution of unemployment rates in the population is symmetric and bell shaped, 95% of the time, the unemployment rate is between _____ and ______ percent

Solution

mean p = (4.2+4.7 +5.4 +5.8 +4.9)/5 = 5

standard deviation = 0.62048

standard error by dividing the standard deviation by the square root of the sample size: = 0.62048/sqrt(5) =0.2775

Compute the margin of error by multiplying the standard error by 1.96 : 1.96 *0.2775 = 0.5438

Compute the confidence interval by adding the margin of error to the mean from Step 1 and then subtracting the margin of error from the mean: 5 +/ 0.5438 = 4.456 % to 6.5438 %

the unemployment rate is between 4.456% and 6.5438 percent