2 A certain packet of mixed lupinus seeds will produce flowe

2. A certain packet of mixed lupinus seeds will produce flowers that are blue (aka bluebonnet), maroon, and white in the ratio of 6:3:1 (one flower per seed). A total of 100 seeds are planted and all germinate, yielding the following results

Blue

Maroon

White

52

36

12

If the null hypotheses is true (the flowers bloom in the 6:3:1) ratio, what are the expected counts for each color of flower for the 100 seeds?

Complete the chi-square goodness of fit test for this data.

Write a conclusion to this data.

Solution

a)

The expected counts are 60, 30, 10, respectively for blue, maroon, white.

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b)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
52   60   1.066666667  
36   30   1.2  
12   10   0.4  

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    2.666666667      
          
As df = a - 1,           
          
a =    3      
df = a - 1 =    2      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    5.991464547      
          
Also, the p value is          
          
p =    0.263597138      
          
Thus, comparing chi^2 and chi^2(crit) [or, p > 0.05], we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that the flowers bloom at a ratio that is not 6:3:1. [CONCLUSION]