Question

Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of three months. Assume that the underlying population distribution is normal.

1. What distribution should you use for this problem? Why?

2. Construct a 99\% confidence interval for the population mean length of time using training wheels.

Answer 1

Solution:

Given:

Sample Size = n = 14

Sample mean = months

Sample standard deviation = s = 3 months

the underlying population distribution is normal.

Part 1. What distribution should you use for this problem? Why?

We use t distribution.

Since sample size = n = 14 is small ( < 30) and population is normally distributed with  unknown standard deviation.

Part 2. Construct a 99% confidence interval for the population mean length of time using training wheels.

Formula:

where

tc is t critical value for c = 99%  confidence level

Thus two tail area = 1 - c = 1 - 0.99 = 0.01

df = n - 1 =  14- 1 = 13
Look in  t table for df = 13 and two tail area = 0.01 and find t critical value

tc = 3.012

Thus

Thus

( Round final answer to specified number of decimal places)