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]
