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

Antonia Lavina · Accepted Answer

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

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