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 $\sigma=55.5$ dollars. You would like to be $95 \%$ confident that your estimate is within 2 dollar(s) of average spending on the birthday parties. How many moms do you have to sample? Do not round mid-calculation. \[ n= \] Try this with your statistics calculator, if you decreases the confidence level, the sample size decreases increases If you decreases the error bound, the sample size decreases increases

Step 1 ：The problem is asking for the sample size needed to estimate the average spending on birthday parties with a certain level of confidence and precision. This is a problem of determining sample size for estimating a population mean. The formula for this is: \[n = \left(\frac{Z*\sigma}{E}\right)^2\] where: n is the sample size, Z is the Z-score corresponding to the desired confidence level (for 95% confidence, Z=1.96), \(\sigma\) is the population standard deviation, E is the desired margin of error.

Step 2 ：We can plug in the given values into the formula: \(\sigma = 55.5\), E = 2, Z = 1.96.

Step 3 ：Solving for n, we get \(n = 2959\).

Step 4 ：Final Answer: The number of moms you have to sample is \(\boxed{2959}\). If you decrease the confidence level, the sample size decreases. If you decrease the error bound, the sample size increases.