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 :

a=r

d=q

c=p

b=s

hope this !

a. the residual plot for model 1 has a random pattern and is a good fit for the data.