Question

You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ=44.1 dollars. You would like to be 90% confident that your estimate is within 1 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?

Answer 1

At least 5263 adults need to be surveyed.

Explanation:

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

`\alpha = (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 the margin of error M as such

`M = z*(\sigma)/(√(n))`

How many parents do you have to sample?

We need to survey at least n parents.

n is found when
`M = 1, \sigma = 44.1`

So

`M = z*(\sigma)/(√(n))`

`1 = 1.645*(44.1)/(√(n))`

`√(n) = 1.645*44.1`

`(√(n))^(2) = (1.645*44.1)^(2)`

`n = 5262.7`

Rounding up

At least 5263 adults need to be surveyed.