Question

In a survey, 101 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $37 and standard deviation of $10. Find the margin of error for a 80% confidence level.

Answer 1

We have the following sample information

n=101 is the sample size

is the sample mean amount spent on the gift

s=10 is the standard deviation of amount spent

We will estimate the population standard deviation using the sample

The standard error of mean is

Since the sample size is greater than 30, we can say that the distribution of sample mean is normal.

The significance level for 80% confidence level is

The right tail critical value is

Using the standard normal tables for z=1.28, we get P(Z<1.28)=0.90

Hence

The margin of error for a 80% confidence interval is

ans: The margin of error for a 80% confidence interval is $1.2736