Question

Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 29 days of operation shows a sample mean of 300 rooms occupied per day and a sample standard deviation of 35 rooms.

1. What is the point estimate of the population variance?
   
   
2. Provide a 90% confidence interval estimate of the population variance (to 1 decimal).
   (  ,  )
   
3. Provide a 90% confidence interval estimate of the population standard deviation (to 1 decimal).
   (  ,  )

Answer 1

Solution :

Given that,

s = 35

(a)

Point estimate = s² = 1225

(b)

²_R = ²_/2,df = 41.337

²_L = ²_{1 - /2,df} = 16.928

The 90% confidence interval for ² is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

28 * 1225 / 41.337 < ² < 28 * 1225 / 16.928

829.8 < ² < 2026.2

(829.8 , 2026.2)

(c)

The 90% confidence interval for is,

28.8 < < 45.0

(28.8 , 45.0)