Question

What would the samples variance be ?  

Dealing with lines, and customer perceptions about wait, is an important customer service challenge. Both public and private institutions could use quantitative methods as a way to assess and analyze solutions.

In this case study, the Westland Post Office studied its waiting times for customer on Saturday morning for a year. The researcher found that the distribution of wait times was approximately normal, with a standard deviation of 7.2 minutes for using individual lines at its seven service windows (this is your hypothetical standard deviation for the purposes of this problem). Please be sure to convert to a variance. Based upon employee brainstorming on how to reduce waits, this post office experimented with a single main waiting line for one Saturday morning, and the researcher randomly sampled 25 customers serviced on the Saturday, finding a sample standard deviation of 3.5 minutes. Please be sure to convert to a variance.

Answer 1

The researcher found that the distribution of wait times was approximately normal, with a standard deviation of 7.2 minutes.

So this is population standard deviation i.e. = 7.2

So population variance = = 7.2² = 51.84

From sample of 25 customers, standard deviation is found to be 3.5.

So this is sample standard deviation = s = 3.5

Hence sample variance = s² = 3.5² = 12.25