Question

In a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $34 and standard deviation of $4. Find the margin of error at a 99%-confidence level. Give your answer to two decimal places.

a. $2.62
b. $1.88
c. $3.89
d. $2.74

Answer 1

The margin of error can be calculated using the formula: Margin of Error = (Critical Value) x (Standard Deviation). Given that the sample mean is $34 and the standard deviation is $4, we need to find the critical value for a 99% confidence level.

Step-by-step explanation:

The margin of error can be calculated using the formula:

Margin of Error = (Critical Value) x (Standard Deviation)

Given that the sample mean is $34 and the standard deviation is $4, we need to find the critical value for a 99% confidence level. This critical value can be found using a z-table or a t-table, depending on the sample size. Since the sample size is small (n<30), we will use the t-table.

For a 99% confidence level and 12 degrees of freedom (13-1), the critical value is approximately 2.68. Substituting the values into the margin of error formula:

Margin of Error = (2.68) x (4) = 10.72

Therefore, the margin of error at a 99% confidence level is approximately $10.72.