Question

A survey of several 8 to 10 year olds recorded the following amounts spent on a trip to the mall:

$24.95, $20.44 ,$20.63, $21.78

Construct the 99% confidence interval for the average amount spent by 8 to 10 year olds on a trip to the mall. Assume the population is approximately normal.

Step 1: Calculate the sample mean for the given sample data. Round your answer to two decimal places.

Step 2: Calculate the sample standard deviation for the given sample data. Round your answer to two decimal places.

Step 3: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 4: Construct the 99% confidence interval. Round your answer to two decimal places.

Lower endpoint: Upper endpoint:

Answer 1

Step1:

Sample size = n = 4

Sample mean = = 21.95

Step 2:

Standard deviation = s = 2.09

Stpe 3:

Degrees of freedom = n - 1 = 4 - 1 = 3

Level of significance = 0.01

Critical value = tc = 5.841 ( Using t table)

Step 3:

We have to construct a 99% confidence interval.

Formula is

Here E is a margin of error.

So confidence interval is ( 21.95 - 6.0914 , 21.95 + 6.0914) = > ( 15.86 , 28.04)