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

Required:
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.)
b. What is the estimated proportion of hotel rooms occupied each year?
c. Calculate the test statistic.

Answer:

Step-by-step explanation:

The null hypothesis and alternative hypothesis can be formulated as:

[tex]\mathbf{H_o: P_1 - P_2 \le 0}[/tex]

[tex]\mathbf{H_1 : P_1 -P_2> 0}[/tex]

From the information given:

The sample proportion of rooms occupied for the current year.

[tex]P_1 = \dfrac{1470}{1750}[/tex]

[tex]P_1 = 0.84[/tex]

Sample size [tex]n_1[/tex] = 1750 (total number of rooms for the current year)

The sample proportion of rooms occupied for the previous year.

[tex]P_2 = \dfrac{1440}{1800}[/tex]

[tex]P_2 =0.8[/tex]

Sample size [tex]n_2[/tex] = 1800 (total number of rooms for the previous year)

Thus, the estimated proportion of the hotel rooms occupied each year are:

Current     Previous

0.84            0.80

Since this is a one-sided right-tailed test;

The pooled proportion can  be computed as:

[tex]\hat p= \dfrac{p_1 \times n_1 + p_2 \times n_2}{n_1 + n_2}[/tex]

[tex]\hat p= \dfrac{0.84 \times 1750 + 0.80 \times1800}{1750 +1800}[/tex]

[tex]\hat p=0.8197[/tex]

The standard error SE = [tex]\sqrt{\hat p ( 1- \hat p) ( \dfrac{1}{n_1} + \dfrac{1}{n_2} )}[/tex]

[tex]= \sqrt{0.8197 ( 1-0.8197) ( \dfrac{1}{1750} + \dfrac{1}{1800} )}[/tex]

[tex]= \sqrt{0.8197 ( 0.1803) (0.00112698 )}[/tex]

[tex]=0.0129[/tex]

Finally, the test statistics is calculated as:

[tex]Z_{calc} = \dfrac{(0.84 - 0.8)}{0.0129}[/tex]

[tex]Z_{calc} = 3.101[/tex]

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