Answer:
Correct option is (c). 1.873.
Step-by-step explanation:
The hypothesis can be defined as:
H₀: There is no difference between the two proportions.
Hₐ: There is a difference between the two proportions.
Given:
[tex]X_{1} = 160,\ n_{1}=200\\X_{2} = 144,\ n_{2}=200[/tex]
The sample proportion of youthful gamers who tried the new Z-Box-Plus game and rated it "excellent," is:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}} =\frac{160}{200} =0.80[/tex]
The sample proportion of adult gamers who tried the new Z-Box-Plus game and rated it "excellent," is:
[tex]\hat p_{2}=\frac{X_{2}}{n_{2}} =\frac{144}{200} =0.72[/tex]
The population proportion of gamers who rated the game as "excellent" is:
[tex]P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}} =\frac{160+144}{200+200}= 0.76[/tex]
The test statistic is:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{P(1-P)[\frac{1}{n_{1}}+\frac{1}{n_{2}} ]} } =\frac{0.80-0.72}{\sqrt{0.76(1-0.76)[\frac{1}{200}+\frac{1}{200} ]} }=1.873[/tex]
Thus, the value of the test statistic is 1.873.
The correct option is (c).
