Question

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.

Answer 1

Answer:

$z=\frac{0.22-0.475}{\sqrt{0.333(1-0.333)(\frac{1}{50}+\frac{1}{40})}}=-2.549$    

Step-by-step explanation:

Data given and notation    

$X_{1}=11$ represent the number of men who believe that sexual discrimination is a problem  

$X_{2}=19$ represent the number of women who believe that sexual discrimination is a problem

$n_{1}=50$ sample 1 selected  

$n_{2}=40$ sample 2 selected  

$p_{1}=\frac{11}{50}=0.22$ represent the proportion estimated of men  who believe that sexual discrimination is a problem

$p_{2}=\frac{19}{40}=0.475$ represent the proportion estimated of female who believe that sexual discrimination is a problem

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)    

$p_v$ represent the value for the test (variable of interest)  

Concepts and formulas to use    

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:    

Null hypothesis:$p_{1} = p_{2}$    

Alternative hypothesis:$p_{1} \neq p_{2}$    

We need to apply a z test to compare proportions, and the statistic is given by:    

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$   (1)  

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{11+19}{50+40}=0.333$  

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.    

3) Calculate the statistic  

Replacing in formula (1) the values obtained we got this:    

$z=\frac{0.22-0.475}{\sqrt{0.333(1-0.333)(\frac{1}{50}+\frac{1}{40})}}=-2.549$