A government agency reported that in 2020, 5.6% of people with a bachelor's degree and 9.4% of people with a high school diploma but no college were unemployed. Suppose that the reported percentages were based on independently selected representative samples of 500 people with a bachelor's degree and 500 people with a high school degree but no college.
Construct a 95% confidence interval for the difference in the proportion who were unemployed for these two groups. (Use Bachelor's Degree − High School Diploma Only. Enter your answer using interval notation. Round your numerical values to four decimal places.)
Guide On Rating System
Vote
To construct a confidence interval for the difference in proportions, we can use the formula:
CI = (p1 - p2) ± z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
Where:
p1 = proportion of people with a bachelor's degree unemployed
p2 = proportion of people with a high school diploma but no college unemployed
n1 = sample size of people with a bachelor's degree
n2 = sample size of people with a high school diploma but no college
z = z-score corresponding to the desired confidence level (95% confidence level = 1.96)
Based on the given information, we have:
p1 = 0.056
p2 = 0.094
n1 = 500
n2 = 500
z = 1.96
Now we can plug these values into the formula and calculate the confidence interval:
CI = (0.056 - 0.094) ± 1.96 * sqrt((0.056 * (1 - 0.056) / 500) + (0.094 * (1 - 0.094) / 500))
CI = (-0.038) ± 1.96 * sqrt(0.0001064 + 0.0000846)
CI = (-0.038) ± 1.96 * sqrt(0.000191)
CI = (-0.038) ± 1.96 * 0.0138302
CI = (-0.038) ± 0.0270597
CI ≈ (-0.06506, -0.01094)
Therefore, the 95% confidence interval for the difference in the proportion of people who were unemployed for those with a bachelor's degree and those with a high school diploma but no college is approximately (-0.0651, -0.0109).
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99