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).

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 level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

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

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.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743