Consider the following to answer the question(s) below:
EU (European Union) countries report that 46% of their labour force is female. The United Nations wants to determine if the percentage of females in the Canadian labour force is the same. Representatives from Statistics Canada plan to check a random sample of over 10,000 employment records on file to estimate the percentage of females in the Canadian labour force.
-They actually select a random sample of 525 employment records, and find that 229 of the people are females. The 90% confidence interval is
A) 0.4006 to 0.4718.
B) 0.2747 to 0.5973.
C) 0.1776 to 0.6944.
D) 0.4235 to 0.5679.
E) 0.1243 to 0.7100.

Question

Quizplus · Accepted Answer

The confidence interval for the proportion of females in the Canadian labour force can be calculated using the formula for a confidence interval for a proportion: $$CI = \hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$ where $\hat{p} = \frac{229}{525}$ is the sample proportion, $n = 525$ is the sample size, and $Z_{\alpha/2}$ is the Z-score corresponding to the desired confidence level (for 90% confidence, typically around 1.645). Plugging in the numbers, the interval that matches the calculation is option A) 0.4006 to 0.4718.

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