Question

Researchers measured the bone mineral desnsity of the spines of 94 women who had taken teh drug CEE. The mean was 1.016 g/cm2, and the standard deviation was 0.155 g/cm2. What is the 95% confidence interval for the mean?

Answer 1

Answer:

The 95% confidence interval for the mean is between 0.985g/cm² and 1.047 g/cm².

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.025 = 0.975$, so $z = 1.96$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96*\frac{0.155}{\sqrt{94}} = 0.0310$

The lower end of the interval is the mean subtracted by M. So it is 1.016 - 0.0310 = 0.985 g/cm²

The upper end of the interval is the mean added to M. So it is 1.016 + 0.0310 = 1.047 g/cm²

The 95% confidence interval for the mean is between 0.985g/cm² and 1.047 g/cm².