Question

Data from a 2006 GSS subsample show that the mean number of children per respondent was 1.87, with a standard deviation of 1.64. A total of 1,494 people answered this question. Estimate the population mean number of children per adult using a 90% confidence interval. We our 90% confident that the population mean number of children per adult is between

Answer 1

Answer:

We are 90% confident that the population mean number of children per adult is between 1.80 and 1.94.

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:

$\alpha = \frac{1-0.9}{2} = 0.05$

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 $1-0.05 = 0.95$, so $z = 1.645$

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.

$M = 1.645*\frac{1.64}{\sqrt{1494}} = 0.07$

The lower end of the interval is the sample mean subtracted by M. So it is 1.87 - 0.07 = 1.80 children

The upper end of the interval is the sample mean added to M. So it is 1.87 + 0.07 = 1.94 children.

We are 90% confident that the population mean number of children per adult is between 1.80 and 1.94.