An experienced goldfish breeder receives two unusual male goldfish. One is black rather than gold, and the other has a single tail fin rather than a split tail fin. The breeder crosses the black male to a female that is gold. All the F₁ are gold. She also crosses the single-finned male to a female with a split tail fin. All the F₁ have a split tail fin. She then crosses the black male to F₁ gold females and, separately, crosses the single-finned male to F₁ split-finned females. The results of the crosses are shown below.
  Black male x F₁ gold female:
    Gold         32
    Black        34
  Single-finned male x F₁ split-finned female:
    Split fin        41
    Single fin     39
Use chi-square analysis to test your hereditary hypothesis for each trait.

If a chi-square test produces a chi-square value of 7.83 with 4 degrees of freedom,

Is the result sufficient to reject the chance hypothesis?

If a chi-square test produces a chi-square value of 7.83 with 4 degrees of freedom,

In what interval range does the P value fall?

Researchers cross a corn plant that is pure-breeding for the dominant traits colored aleurone (C1), full kernel (Sh), and waxy endosperm (Wx) to a pure-breeding plant with the recessive traits colorless aleurone (c1), shrunken kernel (sh), and starchy (wx). The resulting F₁ plants were crossed to pure-breeding colorless, shrunken, starchy plants. Counting the kernels from about 30 ears of corn yields the following data.

What is the order of these genes in corn?

Researchers cross a corn plant that is pure-breeding for the dominant traits colored aleurone (C1), full kernel (Sh), and waxy endosperm (Wx) to a pure-breeding plant with the recessive traits colorless aleurone (c1), shrunken kernel (sh), and starchy (wx). The resulting F₁ plants were crossed to pure-breeding colorless, shrunken, starchy plants. Counting the kernels from about 30 ears of corn yields the following data.

Perform a chi-square test to determine if these data show significant deviation from the expected phenotype distribution.

Experimental Insight 2.1 describes data, collected by a genetics class like yours, on the numbers of kernels of different colors in bicolor corn. To test the hypothesis that the presence of kernels of different colors in each ear is the result of the segregation of two alleles of a single gene, the class counted 12,356 kernels and found that 9304 were yellow and 3052 were white. Use chi-square analysis to evaluate the fit between the segregation hypothesis and the class results.

The basis for rejecting any null hypothesis is arbitrary. The researcher can set more or less stringent standards by deciding to raise or lower the p value used to reject or not reject the hypothesis. In the case of the chi-square analysis of genetic crosses, would the use of a standard of p = 0.10 be more or less stringent about not rejecting the null hypothesis? Explain.

To assess Mendel's law of segregation using tomatoes, a true-breeding tall variety (SS) is crossed with a true-breeding short variety (ss). The heterozygous F₁ tall plants (Ss) were crossed to produce two sets of F₂ data, as follows.

From the above analysis, what can you conclude about the importance of generating large datasets in experimental conditions?

To assess Mendel's law of segregation using tomatoes, a true-breeding tall variety (SS) is crossed with a true-breeding short variety (ss). The heterozygous F₁ tall plants (Ss) were crossed to produce two sets of F₂ data, as follows.

Using the X² test, analyze the results for both datasets. Calculate X² values and estimate the p values in both cases.