Respuesta :
Answer:
Following are the solution to the given question:
Step-by-step explanation:
[tex]n = 500\\\\X = 360\\\\\hat{p}=\frac{X}{n}\\\\[/tex]
[tex]=\frac{360}{500}\\\\=\frac{36}{50}\\\\= 0.72[/tex]
Calculating the Null hypothesis:
[tex]H_{0}:p=0.76[/tex]
Calculating the Alternative hypothesis:
[tex]H_{1}:p\neq 0.76[/tex]
[tex]\therefore \\\\p = 0.76\\\\\because \\\\ q = 1 - p = 1 - 0.76 = 0.24\\\\Test \ \ statistics\ Z = \frac{(\hat{p}-p)}{\sqrt{\frac{pq}{n}}}\\\\[/tex]
[tex]= \frac{(0.72-0.76)}{\sqrt{\frac{(0.76\times 0.24)}{500}}}\\\\= -\frac{0.04}{\sqrt{\frac{0.1824}{500}}}\\\\= -\frac{0.04}{\sqrt{0.000365}}\\\\= -\frac{0.04}{0.019}\\\\= -2.10[/tex]
[tex]\alpha=0.05\\\\p-value = 0.0179\\\\p-value< 0.05\\\\\therefore \\\\0.0179 < 0.05, \text{reject null hypothesis}\\\\P \leq 0.05,\text{reject null hypothesis} \ H_{0}\ at\ \alpha=0.05 \\\\\alpha=0.10\\\\ p-value = 0.0179\\\\p-value< 0.10\\\\\therefore \ 0.0179 < 0.10, \text{reject null hypothesis}\\\\P > 0.10,\text{we do not reject null hypothesis}\ H_{0} \ at \alpha=0.10 .[/tex]
