How would you solve these problems? I am confused about what it is asking and how to start it. A step by step process with explanation would be greatly appreciated. Also, are there any simple ways to work out the problems without getting confused, or is there a way to know what methods to use to solve certain problems? Thank you.
1) A cross between two heterozygous organisms produces progeny with a phenotypic ratio of 253.65. Use a Chi square test to see if the data fits an expected 3:1 ratio. Do you accept or reject the data as fitting the ratio?
2) Cystic fibrosis is an autosomal recessive disorder. A male of unknown genotype (whose brother has the disease, but parents don't) has two children with a female of unknown genotype (whose sister has the disease, but parents don't), neither child has the disease. If they decide to have another child, what is the probAbility that the child will have the disease? Draw out the pedigrees.
3) In sesame, the one-pod condition (P) is dominant to the three-pod condition (p), and normal leaf (L) is dominant over wrinkled leaf (l). The two characters are inherited independently. A cross between two members of F1 generation produces the following progeny: 318 one-pod normal, 185 one-pod wrinkled, 323 three-pod normal and 184 three-pod wrinkled. Determine, using chi-square analysis whether the data fits the typical 9:3:3:1 ratio.
Sure! Let's go through each problem step by step and explain how to solve it.
1) To solve this problem, we will use a Chi square test to determine if the observed data fits the expected ratio. The expected ratio in this case is 3:1.
Step 1: Set up the null and alternative hypotheses. In this case, the null hypothesis is that the data fits the expected 3:1 ratio, while the alternative hypothesis is that the data does not fit the expected ratio.
Step 2: Calculate the expected values for each category. Since we have a phenotypic ratio of 253.65, we can calculate the expected values by multiplying this ratio by the total number of progeny. The expected values for the two categories (phenotype A and phenotype a) would be (253.65 * 3) and (253.65 * 1), respectively.
Step 3: Calculate the Chi square test statistic. The formula for the Chi square test statistic is:
X^2 = Σ([(Observed value - Expected value)^2] / Expected value)
You would calculate this for each category and sum them up. Remember, the Σ symbol represents summation, so you need to calculate this for each category.
Step 4: Calculate the degrees of freedom. In this case, the degrees of freedom would be (number of categories - 1). Since we have 2 categories (phenotype A and phenotype a), the degrees of freedom would be 1.
Step 5: Look up the critical Chi square value from the Chi square distribution table for your chosen significance level and degrees of freedom. If the calculated Chi square test statistic value is greater than the critical value, we reject the null hypothesis. If it is smaller, we accept the null hypothesis.
That's the step-by-step process to solve problem 1 using the Chi square test.
Now, moving on to your second question:
2) To determine the probability of a child having cystic fibrosis, we need to analyze the genotypes of the parents.
Step 1: Construct a pedigree chart to represent the information given about the parents, siblings, and children. This will help visualize the inheritance pattern.
Step 2: Analyze the pedigree chart and determine the possible genotypes of the parents. In this case, the male is of unknown genotype but his brother has the disease, suggesting that he is a carrier of the recessive allele. The female is also of unknown genotype, but her sister has the disease, suggesting she is also a carrier.
Step 3: Determine the genotypes of the children based on the genotypes of the parents. Since neither child has the disease, they must be either carriers (heterozygous) or have neither allele (homozygous recessive).
Step 4: Use the Punnett square to determine the genotypes of the possible offspring. Since cystic fibrosis is an autosomal recessive disorder, you will need to use a 2x2 Punnett square.
Step 5: Calculate the probability of having a child with the disease from the Punnett square results. This can be done by counting the number of possible genotypes that result in cystic fibrosis and dividing it by the total number of possible genotypes.
That's the step-by-step process to determine the probability of a child having cystic fibrosis using pedigree analysis.
Lastly, let's address problem 3:
3) In this problem, we are given information about the inheritance of two different traits in sesame plants. We want to determine if the observed data fits the expected 9:3:3:1 ratio.
Step 1: Set up the null and alternative hypotheses. The null hypothesis is that the data fits the expected 9:3:3:1 ratio, while the alternative hypothesis is that the data does not fit the expected ratio.
Step 2: Calculate the expected values for each category. For a 9:3:3:1 ratio, you would multiply the total number of progeny by the corresponding ratios (9/16, 3/16, 3/16, and 1/16) to get the expected values for each category.
Step 3: Calculate the Chi square test statistic using the formula mentioned earlier. Calculate the value for each category and sum them up.
Step 4: Calculate the degrees of freedom. In this case, the degrees of freedom would be (number of categories - 1). Since we have 4 categories, the degrees of freedom would be 3.
Step 5: Look up the critical Chi square value from the Chi square distribution table for your chosen significance level and degrees of freedom. If the calculated Chi square test statistic value is greater than the critical value, we reject the null hypothesis. If it is smaller, we accept the null hypothesis.
That's the step-by-step process to determine whether the data fits the typical 9:3:3:1 ratio using Chi square analysis.
As for your question about simple ways to work out these problems without getting confused, it really helps to break down the problem into steps, as we've done above. Additionally, understanding the underlying principles and concepts behind each problem is crucial. Familiarizing yourself with genetic inheritance patterns, Punnett squares, and Chi square analysis can make these types of problems much more manageable.
I hope this explanation helps! Let me know if you have any further questions.