3. Airbnb hosts wish to learn the average length of stay of all visitors that are under the age of 30. Astatistician determines that to calculate a 95% confidence level estimate of the average length of stayto within +/- 1.5 days, a total of 95 young visitors' check-in/check-out records will have to beexamined. How many records should be looked at to obtain a 95% confidence level estimate to within+/- 0.5 days?

Answered: 3. Airbnb hosts wish to learn the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Airbnb hosts wish to learn the average length of stay of all visitors that are under the age of 30. A
statistician determines that to calculate a 95% confidence level estimate of the average length of stay
to within +/- 1.5 days, a total of 95 young visitors' check-in/check-out records will have to be
examined. How many records should be looked at to obtain a 95% confidence level estimate to within
+/- 0.5 days?

Expert Solution

Step 1

Solution:

We are given that total of n= 95 young visitors for 95% confidence level with the average length of stay to within $\pm 1.5$ days of all visitors that are under the age of 30.

Using this information we find the population variance.

$n = \frac{{Z_{α / 2}}^{2} \times σ^{2}}{E^{2}} H e r e n = 95 S a m p l e s i z e E = 1.5 m a r g i n o f e r r o r A t α = 0.05 Z_{α / 2} = Z_{0.025} = 1.96 F r o m Z t a b l e 95 = \frac{1 . 96^{2} \times σ^{2}}{1 . 5^{2}} 95 = \frac{3.8416 \times σ^{2}}{2.25} σ^{2} = \frac{95 \times 2.25}{3.8416} σ^{2} = \frac{213.75}{3.8416} σ^{2} = 55.6409$