France Unemployment Rate: MCQ Homework

[little neutrino]

Homework Statement

One month the actual unemployment rate in France was 13.4%. If during that month you took a SRS of 100 Frenchmen and constructed a confidence interval estimate of the unemployment rate, which of the following would have been true?

A) The center of the interval was 13.4.
B) The interval contained 13.4.
C) A 99% confidence interval estimate contained 13.4.
D) The z-score of 13.4 was between +-2.576.
E) None of the above are true statements.

Homework Equations

The Attempt at a Solution

Since (unemployed, not unemployed) are 2 variables, I think the confidence interval for a proportion applies here. Since np = 13.4 > 10 and n(1-p) = 100 - 13.4 > 10, a normal distribution can be used to approximate the binomial distribution. Then shouldn't A, B, C, and D all be correct? It is a simple random sample, and the sample size is less than 10% of the French population. But the answer key says the exact opposite; E is the correct answer. Could somebody explain why? Thanks! :)

 

[Ray Vickson]

Homework Statement

One month the actual unemployment rate in France was 13.4%. If during that month you took a SRS of 100 Frenchmen and constructed a confidence interval estimate of the unemployment rate, which of the following would have been true?

A) The center of the interval was 13.4.
B) The interval contained 13.4.
C) A 99% confidence interval estimate contained 13.4.
D) The z-score of 13.4 was between +-2.576.
E) None of the above are true statements.

Homework Equations

The Attempt at a Solution

Since (unemployed, not unemployed) are 2 variables, I think the confidence interval for a proportion applies here. Since np = 13.4 > 10 and n(1-p) = 100 - 13.4 > 10, a normal distribution can be used to approximate the binomial distribution. Then shouldn't A, B, C, and D all be correct? It is a simple random sample, and the sample size is less than 10% of the French population. But the answer key says the exact opposite; E is the correct answer. Could somebody explain why? Thanks! :)

Basically: in a random sample, the observed unemployment rate could vary from 0% to 100%. That is unlikely, but rare things DO happen. Even a 99% confidence interval could miss the 13.4% figure, because 99% confidence intervals will contain the true mean 99% of the time. That means they will fail to contain the true mean 1% of the time, and this could be one such time.

 

[little neutrino]

Basically: in a random sample, the observed unemployment rate could vary from 0% to 100%. That is unlikely, but rare things DO happen. Even a 99% confidence interval could miss the 13.4% figure, because 99% confidence intervals will contain the true mean 99% of the time. That means they will fail to contain the true mean 1% of the time, and this could be one such time.

Ah I see... Thanks! :)