Winter visitors are extremely important to the economy of so

Winter visitors are extremely important to the economy of southwest florida. hotel occupancy is an often-reported measure of visitor volume and activity. Hotel occupanct data for February in two consecutive years are as follows

a. Formulate the hypothesis test that can be used to determine if there has been an increase in the proportion of rooms occupied over the one-year period.

b. What is the estimated proportion of hotel rooms occupied each year?

c. Using a 0.05 level of significance, what is your hypothesis test conclusion? What is the p-value?

d. What is the 95% confidence interval estimate of the change in occupancy for the one-year period? Do you think area officials would be pleased with the results?

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 < p2
Alternate, has been an increase in the proportion of rooms occupied H1: p1 > p2
Test Statistic
Sample 1 : X1 =1470, n1 =1750, P1= X1/n1=0.84
Sample 2 : X2 =1458, n2 =1800, P2= X2/n2=0.81
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.825
Q^ Value For Proportion= 1-P^=0.175
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.84-0.81)/Sqrt((0.825*0.175(1/1750+1/1800))
Zo =2.351
| Zo | =2.351
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =2.351 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 2.3508 ) = 0.00937
Hence Value of P0.05 > 0.00937,Here we Reject Ho

we have evidence to indicate that has been an increase in the proportion of rooms occupied