A researcher has developed a theoretical model for predicting eye color. After examining a random sample of​ parents, she predicts the eye color of the first child. The table below lists the eye colors of offspring. Based on her​ theory, she predicted that​ 87% of the offspring would have brown​ eyes, 8% would have blue​ eyes, and​ 5% would have green eyes. Use a 0.05 significance level to test the claim that the actual frequencies correspond to her predicted distribution.                       Brown Eyes Blue Eyes Green Eyes   Frequency          135                   20                    0 a. State Upper H 0 .     A. p Subscript Brown Baseline equals 0.87 comma p Subscript Blue Baseline equals 0.08 comma p Subscript Green Baseline equals 0.05     B. p Subscript Brown Baseline equals 0.87 comma p Subscript Blue Baseline equals 0.05 comma p Subscript Green Baseline equals 0.08     C. p Subscript Brown Baseline equals 0.08 comma p Subscript Blue Baseline equals 0.87 comma p Subscript Green Baseline equals 0.05     D. p Subscript Brown Baseline equals 87 comma p Subscript Blue Baseline equals 8 comma p Subscript Green Baseline equals 5     b. Find the sum of the observed​ frequencies: nothing   ​(enter a whole​ number)   c. Calculate the expected frequency for each color​ (give 2 decimal​ places)      ​ Brown: nothing     ​Blue: nothing     ​Green: nothing   d. Calculate the test statistic. Which of these options is closest to its​ value?     A. chi squared equals 11.52     B. chi squared equals 12.41     C. chi squared equals 11.05     D. chi squared equals 13.38     e. State the value of the critical​ value: nothing   ​(give 3 decimal​ places)   f. State the technical conclusion.     A. Do not reject Upper H 0     B. Reject Upper H 0     g. State the final conclusion.     A. There is sufficient evidence to warrant rejection of the claim.   B. There is not sufficient sample evidence to support the claim.   C. There is not sufficient evidence to warrant rejection of the claim.   D. The sample data support the claim.   h. Does her theoretical model appear to be​ accurate?

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A researcher has developed a theoretical model for predicting eye color. After examining a random sample of​ parents, she predicts the eye color of the first child. The table below lists the eye colors of offspring. Based on her​ theory, she predicted that​ 87% of the offspring would have brown​ eyes, 8% would have blue​ eyes, and​ 5% would have green eyes. Use a 0.05 significance level to test the claim that the actual frequencies correspond to her predicted distribution.
 
                    Brown Eyes Blue Eyes Green Eyes  
Frequency         
135
                 
20
                  
0
a. State
Upper H 0
.
 
 
A.
p Subscript Brown Baseline equals 0.87 comma p Subscript Blue Baseline equals 0.08 comma p Subscript Green Baseline equals 0.05
 
 
B.
p Subscript Brown Baseline equals 0.87 comma p Subscript Blue Baseline equals 0.05 comma p Subscript Green Baseline equals 0.08
 
 
C.
p Subscript Brown Baseline equals 0.08 comma p Subscript Blue Baseline equals 0.87 comma p Subscript Green Baseline equals 0.05
 
 
D.
p Subscript Brown Baseline equals 87 comma p Subscript Blue Baseline equals 8 comma p Subscript Green Baseline equals 5
 
 
b. Find the sum of the observed​ frequencies:
nothing
 
​(enter a whole​ number)
 
c. Calculate the expected frequency for each color​ (give 2 decimal​ places)
 
   ​ Brown:
nothing
   

​Blue:

nothing
   

​Green: nothing

 
d. Calculate the test statistic. Which of these options is closest to its​ value?
 
 
A.
chi squared equals

11.52

 
 
B.
chi squared equals

12.41

 
 
C.
chi squared equals

11.05

 
 
D.
chi squared equals

13.38

 
 
e. State the value of the critical​ value:
nothing
 
​(give 3 decimal​ places)
 
f. State the technical conclusion.
 
 
A.
Do not reject Upper H 0
 
 
B.
Reject Upper H 0
 
 
g. State the final conclusion.
 
 
A.
There is sufficient evidence to warrant rejection of the claim.
 
B.
There is not sufficient sample evidence to support the claim.
 
C.
There is not sufficient evidence to warrant rejection of the claim.
 
D.
The sample data support the claim.
 
h. Does her theoretical model appear to be​ accurate?
 
 
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