A statistician chooses 27 randomly selected dates, and when examining the occupa

Question

A statistician chooses 27 randomly selected dates, and when examining the occupancy records of a particular motel for those dates, finds a standard deviation of 5.86 rooms rented. If the number of rooms rented is normally distributed, (a) find the 80% confidence interval for the population standard deviation of the number of rooms rented, (b) Above what value would one expect 25% of all variances from this population to fall? (c) What Reliability Coefficient would cut off the lower 95% of the variances from this population? (d) Above what value would 5% of the variances from this population fall?

Explanation / Answer

given sample size n=27

random variable x: no. of rooms rented

SD=5.86 rooms

SD follows Chi-sq distribution

(a) (1-)*100% CI:

(n1)s22/2 2 (n1)s221/2

FORMULA:

(b) 40.19

formula:

Variance value such that P(Variance>population variance)= Chi-sq inverse at the given significance*variance value/(n-1)

=CHISQ.INV.RT(0.25,26)*5.86^2/26

(c) 20.31

formula=CHISQ.INV(0.05,26)*5.86^2/26

(d) 51.36

formula==CHISQ.INV(0.95,26)*5.86^2/26

lower limit upper limit 5.010534 7.185601

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