Chi-Squared Test for Pea Plant Crosses: Calculate, Interpret, and Analyze

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In summary, the cross between two types of pea plants shows no significant deviation from the expected ratios, with a calculated value of \chi ^2 = 0.28, which is smaller than the critical value of 6.25. The probability value in the distribution table suggests that there is a high probability that the observed data is not significantly different from the expected ratios.
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Homework Statement



In a cross between two types of pea plants, one heterozygous for the round yellow seed condition, and the other, pure breeding with wrinkled green seeds, the following offsprings were recorded;

Round yellow peas-- 108
Round green peas-- 102
Wrinkled yellow peas--105
Wrinkled green peas-- 101


Homework Equations



[tex]\chi[/tex] ^2 = [tex]\Sigma[/tex] {O-E)^2 / E}

The ratio of a heterozygous cross with a homozygous recessive

The Attempt at a Solution



I calculated the value of [tex]\chi[/tex] ^2 to be 0.28. The degrees of freedom= no. of categories-1 = 3.

I'm a little bit confused on how to relate the calculated value of [tex]\chi[/tex] ^2 to the probability value in the distribution table.

I took the probability value as > 0.1 and got 6.25 according to the data in the table. I'm now assuming that it isn't a significant deviation as the value of [tex]\chi[/tex] ^2 is much smaller than this (0.28).

Can someone please explain this if I'm on the wrong track. Thanks
 
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Thank you for sharing your calculations and reasoning. Your approach seems to be correct. The value of \chi ^2 that you have calculated (0.28) is smaller than the critical value of 6.25, indicating that there is no significant deviation from the expected ratios in the offspring. This means that the observed data is in line with the expected ratios, and the cross between the two types of pea plants is not significantly different from what is expected based on Mendelian genetics.

In terms of relating the calculated value of \chi ^2 to the probability value in the distribution table, it is important to note that the probability value in the table represents the probability of obtaining a \chi ^2 value equal to or greater than the critical value, assuming that there is no true difference between the expected and observed values. In this case, since the calculated value of \chi ^2 is smaller than the critical value, the probability value is greater than 0.1, indicating that there is a high probability that the observed data is not significantly different from the expected ratios.

I hope this helps clarify your understanding. Keep up the good work as a scientist!
 

FAQ: Chi-Squared Test for Pea Plant Crosses: Calculate, Interpret, and Analyze

What is a Chi-Squared Test?

A Chi-Squared Test is a statistical test used to determine whether there is a significant difference between expected and observed values in a data set.

How is a Chi-Squared Test used in pea plant crosses?

In pea plant crosses, a Chi-Squared Test can be used to analyze the ratio of phenotypes that result from a genetic cross. This can help determine if the observed ratio is significantly different from the expected ratio, indicating whether the cross follows Mendelian genetics or not.

How do you calculate a Chi-Squared value for pea plant crosses?

To calculate a Chi-Squared value for pea plant crosses, you need to compare the observed number of each phenotype with the expected number based on Mendelian genetics. The formula for calculating Chi-Squared is (observed-expected)^2/expected, and this calculation is repeated for each phenotype. The individual Chi-Squared values are then summed to get the total Chi-Squared value.

What does the Chi-Squared value represent in a pea plant cross?

The Chi-Squared value represents the degree of deviation from the expected ratio based on Mendelian genetics. A higher Chi-Squared value indicates a greater difference between the observed and expected values, and a lower value indicates a closer match.

How do you interpret the results of a Chi-Squared Test for pea plant crosses?

The results of a Chi-Squared Test for pea plant crosses can be interpreted by comparing the calculated Chi-Squared value with a critical value from a Chi-Squared table. If the calculated value is greater than the critical value, it indicates a significant difference between the observed and expected values, and the null hypothesis (that the cross follows Mendelian genetics) can be rejected. If the calculated value is less than the critical value, there is not enough evidence to reject the null hypothesis.

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