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Content type
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Subject
Statistics
Type
Homework
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1. A survey conducted in a particular state in the US shows that 8 out of 23 women have a
college degree while 9 out of 29 men have a college degree, at α= 0.05, is there is a
difference between the number of women and men with a college degree?
Solution:
Let
be the proportion of women with a college degree and
be the proportion of men
with a college degree. Then

 and



 
 
  
 

      
Hypotheses:
and
The critical values for  are + 1.96 and -1.96 two tail critical region.
Our test statistic










 
,
hence
we do not reject the null hypothesis.
There is no enough evidence to support the claim that there is a difference between the
number of women and men with a college degree.
The p-value for our test statistic is 0.7642.
2. A survey conducted in a particular state in the US shows that 6 out of 23 women have no
children while 6 out of 29 men have no children, at , is there a difference in the
proportion?
Solution:
Let
be the proportion of women without children and
be the proportion of men
without children. Then

 and



 
 
  
 

      
Hypotheses:
and
The critical values for  are + 2.58 and -2.58, two tail critical region.
Our test statistic



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1. A survey conducted in a particular state in the US shows that 8 out of 23 women have a college degree while 9 out of 29 men have a college degree, at α= 0.05, is there is a difference between the number of women and men with a college degree? Solution: Let 𝑝1 be the proportion of women with a college degree and 𝑝2 be the proportion of men with a college degree. Then 𝑋 8 𝑋 9 𝑝̂1 = 1 = = 0.35 and 𝑝̂2 = 2 = = 0.31 𝑛1 23 𝑛2 29 𝑋1 + 𝑋2 8+9 𝑝̅ = = = 0.33 𝑛1 + 𝑛2 23 + 29 𝑞̅ = 1 − 𝑝̅ = 1 − 0.33 = 0.67 Hypotheses: 𝐻0 : 𝑝1 = 𝑝2 and 𝐻1 ...
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