In 2000 there were almost 300,000 Canadians with more than 1 million dollars in financial assets! If the average age of one hundred randomly selected millionaires was 54.8 years with a standard deviation of 7.9 years, what is the 95% confidence interval for the mean age, $\mu$ of all Canadian millionaires?
A) $53.5

Question

In 2000 there were almost 300,000 Canadians with more than 1 million dollars in financial assets! If the average age of one hundred randomly selected millionaires was 54.8 years with a standard deviation of 7.9 years, what is the 95% confidence interval for the mean age, $\mu$ of all Canadian millionaires? 
A) $53.5 < \mu < 56.1$
B) $53.3 < \mu < 56.3$
C) $52.8 < \mu < 56.8$
D) $51.7 < \mu < 57.7$

Quizplus · Accepted Answer

We can use the formula for a confidence interval:
$$\text{CI}=\bar{x} \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$$
where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the critical value from the t-distribution with $n-1$ degrees of freedom and confidence level $1-\alpha$. For a 95% confidence interval, $\alpha=0.05$ and $t_{\alpha/2}=2.0$ for a sample size of 100.

Plugging in the given information, we get:
$$\text{CI}=54.8 \pm 2.0\frac{7.9}{\sqrt{100}}$$
Simplifying, we get:
$$\text{CI}=54.8 \pm 1.58$$
Therefore, the 95% confidence interval for the mean age of all Canadian millionaires is:
$$53.22 < \mu < 56.38$$
which is closest to answer choice B: $53.3 < \mu < 56.3$

In 2000 There Were Almost 300,000 Canadians with More Than μ\muμ

In 2000 There Were Almost 300,000 Canadians with More Than $\mu$