In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 3.8%.Create a 95% confidence interval for the proportion of unemployment.
A)Based on the data,we are 95% confident the proportion of unemployment is between 3.82% and 6.58%.
B)Based on the data,we are 95% confident the proportion of unemployment is between 2.61% and 4.99%.
C)Based on the data,we are 95% confident the proportion of unemployment is between 0% and 8.73%.
D)Based on the data,we are 95% confident the proportion of unemployment is between 2.4% and 5.2%.
E)Based on the data,we are 95% confident the proportion of unemployment is between 3.82% and 5.18%.

Question

Quizplus · Accepted Answer

To calculate a 95% confidence interval for the proportion, we use the formula for the confidence interval of a proportion: $p \pm z\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion (0.038), $n$ is the sample size (1000), and $z$ is the z-score corresponding to a 95% confidence level (approximately 1.96). Plugging in the values: $0.038 \pm 1.96\sqrt{\frac{0.038(1-0.038)}{1000}}$ gives an interval of approximately 0.0261 to 0.0499, or 2.61% to 4.99%.

In April of 2011,the Unemployment Rate in Canada Was Reported