Answer:
Following are the response to the given question:
Step-by-step explanation:
Testing hypothesis:
[tex]H_0: p \geq 0.2 \\\\H_a: p < 0.2[/tex]
When it's a lower tailed test:
[tex]\hat{p}=\frac{x}{n}=\frac{1308}{6967}\approx 0.1877\\\\n= 6967\\\\[/tex]
claimed proportion, [tex]P = 0.2[/tex]
Significance level, [tex]\alpha= 0.01[/tex]
calculating statistics :
[tex]\hat{p}, \sigma_{\hat{p}}=\sqrt{\frac{P \times (1-p)}{n}}\\\\[/tex]
[tex]=\sqrt{\frac{0.2 \times (1-0.2)}{6967}}\\\\ =\sqrt{\frac{0.2 -0.04}{6967}}\\\\ =\sqrt{\frac{0.16}{6967}} \\\\ =\sqrt{2.2965}\approx 1.51[/tex]
