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    An experiment was carried out to investigate the inheritance of grain shapes and colour in maize. The number of each type of grain on a cob were counted (observed number).
    The results are shown in the table below:



    it was predicted that the phenotype would be in the ratio 9 : 3 : 3: 1 and a chi-squared test was used to investigate whether there was a significant difference between the observed results and the expected results.

    Complete the table by calculating the expected number (E) of grains of each phenotype.


    --

    So what I did was:
    the ratio is 9 : 3 : 3 : 1

    For yellow & smooth: 9/16 x 53 = 29.8125
    Yellow & wrinkled: 3/16 x 20= 3.75
    and so on ...

    but my answers are all wrong??
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    What you should have done is:

     \mathrm{For\ Yellow\ and\ Smooth,\ expected\ value} = 100 \times \dfrac{9}{16} = 56.25

    Why 100?

    That is the sum of observed numbers, i.e. 53 + 20 + 17 + 10 = 100

    The expected value tells you, "From a sample of x what number of that should be this category?"
    Spoiler:
    Show
    Think of it like this.

    Firstly, forget the observed numbers.

    If I told you I will give you 16 grains, what would you expect to see of each phenotype?

    Well.. based on your ratios, we would expect to see:
    9 of the Yellow and Smooth
    3 of the Yellow and Wrinkled
    3 of the White and Smooth
    and 1 of the White and Wrinkled.

    Then I actually give you the 16 grains. And what you observe may or may not be different.
    You might observe 14 to be Yellow and Smooth, or 5 to be White and Wrinkled, or whatever.

    The point is, the expected takes into account the whole of the observed, i.e. the sample.
    • Thread Starter
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    (Original post by RMNDK)
    What you should have done is:

     \mathrm{For\ Yellow\ and\ Smooth,\ expected\ value} = 100 \times \dfrac{9}{16} = 56.25

    Why 100?

    That is the sum of observed numbers, i.e. 53 + 20 + 17 + 10 = 100

    The expected value tells you, "From a sample of x what number of that should be this category?"
    Spoiler:
    Show
    Think of it like this.

    Firstly, forget the observed numbers.

    If I told you I will give you 16 grains, what would you expect to see of each phenotype?

    Well.. based on your ratios, we would expect to see:
    9 of the Yellow and Smooth
    3 of the Yellow and Wrinkled
    3 of the White and Smooth
    and 1 of the White and Wrinkled.

    Then I actually give you the 16 grains. And what you observe may or may not be different.
    You might observe 14 to be Yellow and Smooth, or 5 to be White and Wrinkled, or whatever.

    The point is, the expected takes into account the whole of the observed, i.e. the sample.
    Thank you!!
 
 
 
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