The National Agricultural Research Organisation (NARO) operates a sprawling campus with over a hundred laboratories and thousands of employees. It also has a number of smaller branch campuses and city offices around the country.

NARO has just appointed a new Chief Information Officer (CIO), Bill Spence, whose responsibilities include the provision of telecommunications facilities for the organisation. On an induction tour of the organisation Bill notices that there are fax machines in every administrative office he visits and most of the laboratories.

“Does anyone actually use this obsolete technology?” he asked his Executive Officer. “I’ve no idea, but certainly not me.” was the reply.

On further inquiry it became clear that, while NARO probably had a few hundred fax machines, and was paying for telephone accounts for them, there was no central list of fax machines and their phone numbers. There was no clear answer to whether they were being used at all.

Bill asked his Executive Officer to “do some kind of survey” to get an idea of whether any staff still had a legitimate need for fax machines. The survey task was delegated to an ANU Intern in the central administration office, Ashley Lee.

Ashley recommended that a carefully selected representative sample of 200 NARO staff be asked a simple question:

“In the last month, have you sent or received a fax using a NARO fax machine?”

Bill approved the survey and asked that the results be reported as a 95% confidence interval estimate of the proportion of all staff who still used fax machines.

NARO had excellent records of staff job responsibilities, locations and contact details, so it was a straightforward but time-consuming process for Ashley to come up with the representative sample of staff.

The survey question was distributed by email over the CIO’s signature, and quickly received 163 responses. Ashley followed up the remaining 37 staff members by email and telephone. After two weeks she was very pleased to report that the survey had a 100% response rate.

However, every one of the 200 respondents said that they had not sent or received a fax in the previous month!

Question 4a
What is the 95% confidence interval estimate of the proportion of staff who used a fax machine in that period? Show your calculations. Use the Agresti-Coull estimate of the standard error for proportions.

Question 4b
What is the population of interest in this case?