Question

A survey of several 9 to 11 year olds recorded the following amounts spent on a trip to the mall: $20.70, $20.82, $12.32, $19.53, $24.43

Construct the 98% confidence interval for the average amount spent by 9 to 11 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 98% confidence interval. Round your answer to two decimal places.

Answer 1

Step 1 of 4: Calculate the sample mean for the given sample data.

Ans: = 19.56

Calculation:

Sample mean () = (20.70+ 20.82 + 12.32 + 19.53 + 24.43)/5 = 19.56

Step 2 of 4: Calculate the sample standard deviation for the given sample data.

Ans: s= 4.44

Calculation:

Sample standard deviation (s) =

=

Step 3 of 4: Find the critical value that should be used in constructing the confidence interval.

Ans:   = 3.74

Calculation:

degrees of freedom = n-1 = 5-1 = 4

t-value for 98% confidence interval for 2 tails at degree of freedom of 4 = 3.744

Step 4 of 4: Construct the 98% confidence interval.

Ans: Confidence interval is (12.12, 27. 00)

Calculation:

Confidence interval

Upper bound

Lower bound