In a survey, 20 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $30 and standard deviation of $2. Find the margin of error for a 99% confidence level.
To find the margin of error for a 99% confidence level, we need to use the formula:
Margin of Error = Critical Value * Standard Deviation
Step 1: Find the critical value
For a 99% confidence level, we need to find the z-score that corresponds to a 0.99 probability. The z-score can be found using a standard normal distribution table or a statistical calculator. For a 99% confidence level, the critical value is approximately 2.576.
Step 2: Calculate the margin of error
Now, we can calculate the margin of error using the formula mentioned earlier:
Margin of Error = Critical Value * Standard Deviation
Given:
Standard Deviation (σ) = $2
Critical Value (Z) = 2.576
Using the formula, we can calculate the margin of error:
Margin of Error = 2.576 * $2
= $5.152 (rounded to two decimal places)
Therefore, the margin of error for a 99% confidence level is approximately $5.15.
Z = (score-mean)/SEm
SEm = SD/√n
The error would be .005 at each end, which gives you a Z score of ±1.645.
I'll let you do the calculations.