Question

In a survey, 27 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $12. Estimate how much a typical parent would spend on their child's birthday gift (use a 95% confidence level).

Answer 1

Answer:

The 95% confidece estimate for how much a typical parent would spend on their child's birthday gift is between $37.47 and $46.53.

Step-by-step explanation:

The results were roughly normal, so we can find the normal confidence interval.

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.

$M = 1.96*\frac{12}{\sqrt{27}} = 4.53$

The lower end of the interval is the sample mean subtracted by M. So it is 42 - 4.53 = $37.47.

The upper end of the interval is the sample mean added to M. So it is 42 + 4.53 = $46.53.

The 95% confidece estimate for how much a typical parent would spend on their child's birthday gift is between $37.47 and $46.53.