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1. 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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2. Bump!! Bump!! Bump!!
3. What you should have done is:

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.
4. (Original post by RMNDK)
What you should have done is:

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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