Answer:
The value [tex]z = 1.572 [/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 1392[/tex]
The number that test positive in first sample is [tex]k = 1173[/tex]
The second sample size is [tex]n_2 = 1457[/tex]
The number that tested positive in the second sample is [tex]z = 1196[/tex]
The first sample proportion is mathematically represented as
[tex]\r p_1 = \frac{k}{n_1}[/tex]
=> [tex]\r p_1 = \frac{1173}{ 1392}[/tex]
=> [tex]\r p_1 =0.843 [/tex]
The second sample proportion is mathematically represented as
[tex]\r p_2 = \frac{z}{n_2}[/tex]
=> [tex]\r p_2 = \frac{1196}{ 1457}[/tex]
=> [tex]\r p_2 =0.821 [/tex]
The null hypothesis is [tex]\r p_1 = \r p_2[/tex]
The alternative hypothesis is [tex]\r p_1 \ne \r p_2[/tex]
Generally test statistics is mathematically represented as
[tex]z = \frac{(\r p_1 - \r p_2)}{ \sqrt{\frac{\r p_1 (1-\r p_1 )}{n_1} + \frac{\r p_1 (1-\r p_1 )}{n_1} } } }[/tex]
[tex]z = \frac{(0.843 - 0.821)}{ \sqrt{\frac{0.843 (1-0.843 )}{1392} + \frac{0.821 (1-0.821 )}{ 1457} } } }[/tex]
[tex]z = 1.572 [/tex]
