Question

Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel). Hotel occupancy data for February in two consecutive years are as follows.

	Current Year	Previous Year
Occupied Rooms	1,470	1,440
Total Rooms	1,750	1,800

(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. (Let p₁ = population proportion of rooms occupied for current year and p₂ = population proportion of rooms occupied for previous year.)

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ ≠ 0

H₀: p₁ − p₂ ≥ 0

H_a: p₁ − p₂ < 0

    

H₀: p₁ − p₂ ≤ 0

H_a: p₁ − p₂ > 0

H₀: p₁ − p₂ < 0

H_a: p₁ − p₂ = 0

H₀: p₁ − p₂ ≠ 0

H_a: p₁ − p₂ = 0

(b)

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

currentprevious

(c)

Calculate the test statistic. (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, what is your hypothesis test conclusion?

Do not reject

H₀.

There is sufficient evidence to conclude that there has been an increase in the hotel occupancy rate.Reject

H₀.

There is insufficient evidence to conclude that there has been an increase in the hotel occupancy rate.    Reject

H₀.

There is sufficient evidence to conclude that there has been an increase in the hotel occupancy rate.Do not reject

H₀.

There is insufficient evidence to conclude that there has been an increase in the hotel occupancy rate.

(d)

What is the 95% confidence interval estimate of the change in occupancy for the one-year period? (Round your answers to four decimal places.)

to

Do you think area officials would be pleased with the results?

The 95% confidence interval  ---Select--- is completely below is completely above contains zero. This suggests that the occupancy rates for the current year are  ---Select--- lower higher than the occupancy rates for the previous year, therefore the officials would  ---Select--- be not be pleased with the results.

Answer 1

Ans:

a)

H₀: p₁ − p₂ ≤ 0

H_a: p₁ − p₂ > 0

b)

sample proportion for current year=1470/1750=0.84

sample proportion for previous year=1440/1800=0.8

c)pooled proportion=(1470+1440)/(1750+1800)=0.8197

Test statistic:

z=(0.84-0.80)/sqrt(0.8197*(1-0.8197)*((1/1750)+(1/1800)))

z=3.10

p-value=P(z>3.10)=0.0010

Reject H₀.There is sufficient evidence to conclude that there has been an increase in the hotel occupancy rate.

d)

95% confidence interval estimate of the change in occupancy

=(0.84-0.8)+/-1.96*SQRT((0.84*(1-0.84)/1750)+(0.8*(1-0.8)/1800))

=0.04+/-0.0252

=(0.0148, 0.0652)

The 95% confidence interval is completely above zero. This suggests that the occupancy rates for the current year are higher than the occupancy rates for the previous year, therefore the officials would be pleased with the results.