Respuesta :
Answer:
[tex]z=\frac{0.22-0.475}{\sqrt{0.333(1-0.333)(\frac{1}{50}+\frac{1}{40})}}=-2.549[/tex] Â Â
Step-by-step explanation:
Data given and notation  Â
[tex]X_{1}=11[/tex] represent the number of men who believe that sexual discrimination is a problem Â
[tex]X_{2}=19[/tex] represent the number of women who believe that sexual discrimination is a problem
[tex]n_{1}=50[/tex] sample 1 selected Â
[tex]n_{2}=40[/tex] sample 2 selected Â
[tex]p_{1}=\frac{11}{50}=0.22[/tex] represent the proportion estimated of men  who believe that sexual discrimination is a problem
[tex]p_{2}=\frac{19}{40}=0.475[/tex] represent the proportion estimated of female who believe that sexual discrimination is a problem
[tex]\hat p[/tex] represent the pooled estimate of p
z would represent the statistic (variable of interest) Â Â
[tex]p_v[/tex] represent the value for the test (variable of interest) Â
Concepts and formulas to use  Â
We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be: Â Â
Null hypothesis:[tex]p_{1} = p_{2}[/tex] Â Â
Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex] Â Â
We need to apply a z test to compare proportions, and the statistic is given by: Â Â
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] Â (1) Â
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{11+19}{50+40}=0.333[/tex] Â
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other. Â Â
3) Calculate the statistic Â
Replacing in formula (1) the values obtained we got this: Â Â
[tex]z=\frac{0.22-0.475}{\sqrt{0.333(1-0.333)(\frac{1}{50}+\frac{1}{40})}}=-2.549[/tex] Â Â
