Question

A baseball player wants to know his average time running from home to first base. He records the
following five times in seconds:

5.1 4.9 5.1 5.2 5.0

Construct a 95% confidence interval for the mean number of seconds it takes for this baseball player to run from
home to first. Interpret this interval within the context of the problem.

Answer 1

Solution:
Given in the question
A baseball player wants to know his average time running from home to first base. He records the five times in seconds so the sample mean can be calculated as
The sample mean = Xi/n = (5.1+4.9+5.1+5.2+5.0)/5 = 25.3/5 = 5.06
Point estimate = 5.06
Sample standard deviation can be calculated as
Sample standard deviation(S) = sqrt((Xi-mean)^2/(n-1)) = sqrt((5.1-5.06)^2 + (4.9-5.06)^2+(5.1-5.06)^2+(5.2-5.06)^2+(5-5.06)^2)/4) = 0.114
95% confidence interval can be calculated as
Point estimate +/- talpha/2*S/sqrt(n)
Here we will use t-test as the sample size is less than 30 and the population standard deviation is not known
So talpha/2 at alpha=0.05, alpha=0.025 and df = 4 is 2.78
so 95% confidence interval is
5.06+/-2.78*0.114/SQRT(5)
5.06+/-0.1415
So a 95% confidence interval is 4.9185 to 5.2015
So baseball players can be 95% confident for the mean number of seconds it takes for this baseball player to run from home to first is between 4.9185 seconds to 5.2015 seconds.