Margin of error

Question

In a survey, 19 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $43 and standard deviation of $6. Find the margin of error at a 99% confidence level.

Give your answer to two decimal places.

Answer 1

Hi Johanna!

So the formula for margin of error is: Z * σ / √n

In this formula, Z represents the Z-score value necessary to get your desired confidence level; however, in this case, since only 19 people were sampled we want to use a t-statistic (which is adjusted to account for a small sample size < 30). We can get this by looking at a T-statistic distribution table; since your sample size is 19, you would use the row for df = 18 (degrees of freedom = n - 1) and the column for α = 0.01 (α = 1.00 - confidence level).

Once you've found the value of Z (or in this case, T), then you already know the values of σ (SD) and n (sample size), so you should be able to use the above formula to calculate margin of error. Hope this helps!