Question

Hello: Can anybody explain this for me

question:

I have 2 columns with vacation rentals yes or no for 2 columns Winter 2000 Winter 2001

Winter 2000 - has 200 entries and 70 of it rental says "yes" hence proportion of units rented = 70/200 = 0.35

Winter 2001 - has 150 entries and 70 of it rental says "yes" hence proportion of units rented = 70/150= 0.467

Find 95% confidence interval for difference in proportions?

Will Winter 2001 have higher rentals than Winter 2000? (based on the proportion above i can say Yes?)

Answer 1

* Solution :- Given :- n = sample estnes in Column winter 2000 n = sample estoes in column winta 200) x1 = Reate saying ye in 2000 x = Restel saying ye in zool ni= 200 n₂ = 150, 2 70, 2= 70 P = sample poopustion = L = 70 = 0.35 91=1-P = 0.65 P2 = Sumple poportion = mu = 70 -0.467 150 92=1-82=0.533 a) 95% Confidere interval for differexe in proportions is (pi-p2) + Zap P9, P292 200 - PU 12 12 ni M Lower limit = CP. -P2) - Zant 19 For 95% Zan - 1.96 Lower limit = (0.35-0.467)- . (0.35)(0.69), (0.467/0.53 200 150 = -0.117 -(1.96)(0.0529) -0.2207 Lower limit

nin & Upper limit - (p. - p.) + Zavr 91, B2h =(-0./17 + ():96)(0.0529) Upper lipsit = -0.0)33. 95% CI for difference in proportions is. ( -0.2202 -0.0133) b) The problem is to test Ho: P = P2 - Vs Hi P <P₂ Test statistic - z = bi-P2 N N (0,1) V ni m 0.35-0.467 [10,35) (0.65 (0.467)(0.533) 200 150 - 0.l17 0.052g - 2.2117 - Zcas - Table value - At 5% 1.0.5. Z - - Za = -1.64 = 1.64 Decision - As Zcal C - Zx , we reject Ho at 5l develo Conclusion - Winter 2001 have higher restels than winter 2000. !
By just looking at sample proportions we can not say about which proportion is higher.Because sample sizes are different. For this we have to conduct Z test for difference between two proportions.