Question

A survey of several 10 to 13 year olds recorded the following amounts spent on a trip to the mall:

$15.64, $12.62, $26.06

Construct the 95% confidence interval for the average amount spent by 10 to 13  year olds on a trip to the mall. Assume the population is approximately normal.

Step 1 of 4:

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

Step 2 of 4:

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

Step 3 of 4:

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

Step 4 of 4:

Construct the 95% confidence interval. Round your answer to two decimal places.

Answer 1

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

Step II: Calculate the sample standard deviation (s) for the given sample data. Round your answer to two decimal places.

  

  

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

We have c = 0.95 => a = 1-c = 0.05 => a/2 = 0.025 => 1 - a/2 = 0.975

Therefore Z critical value correspond to 0.975 is 1.960

Step IV: Construct the 95% confidence interval. Round your answer to two decimal places.

First we have to compute margin error ME()

Lower Bound (LB) = - ME() = 18.11 - 7.9778 = 10.13

Upper Bound (UB) = + ME() = 18.11 + 7.9778 = 26.09