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 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms.

a. what is the point estimate of the population variance (to nearest whole number)?

b. provide a 90% confidence interval estimate of the population variance (to nearest whole number).

c. provide a 90% confidence interval estimate of the population standard deviation (to 1 decimal).

a)

b)

Rounded to the nearest number would be:

c)

And rounded :

Step-by-step explanation:

Data given and notation

s=30 represent the sample standard deviation

represent the sample mean

n=20 the sample size

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Part a

The best point of estimate for the population variance is the sample variance, so on this case:

Part b

The confidence interval for the population variance is given by the following formula:

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,19)" "=CHISQ.INV(0.95,19)". so for this case the critical values are:

And replacing into the formula for the interval we got:

Rounded to the nearest number would be:

Part c

In order to find the confidence interval for the deviation we just need to take the square root for the interval of the variance, and we got:

And rounded :

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above