Question

Tomato plants have many linked genes. Tall (T) is dominant to dwarf (t) bush height, smooth fruit (F) is dominant to wrinkled fruit (f), and spherical fruit shape (S) is dominant to cylindrical fruit shape (s). Several F1 generation heterozygous tomato plants for all 3 traits are crossed with homozygous recessive tomato plants (a testcross) to verify linkage between the bush height and fruit texture genes.

PhenotypeObserved tomatoes (506 total)Drawf, Smooth fruit, Spherical fruit shape (ttFfSs)36Tall, Wrinkled fruit, Cylindrical fruit shape (Ttffss)41Drawf, Wrinkled fruit, Cylindrical fruit shape (ttffss)207Tall, Smooth fruit, Spherical fruit shape (TtFfSs)222
What is the chi square value for this data to the nearest hundreth (two numbers after the decimal)?

Answer 1

The chi-square value for this data is 1677.21.

Step-by-step explanation:

The chi-square value for this data can be calculated using the formula:

χ^2 = Σ(O - E)^2 / E

Where O is the observed frequency and E is the expected frequency. To calculate the expected frequency, you need to determine the expected phenotypic ratios based on the genetics of the traits being crossed. In this case, the expected phenotypic ratios are:

• Tall, Smooth fruit, Spherical fruit shape (TTFFSS) - 1/16
• Tall, Smooth fruit, Cylindrical fruit shape (TTFFSs) - 2/16
• Tall, Wrinkled fruit, Spherical fruit shape (TTffSS) - 1/16
• Tall, Wrinkled fruit, Cylindrical fruit shape (TTffSs) - 2/16
• Dwarf, Smooth fruit, Spherical fruit shape (ttFFSS) - 2/16
• Dwarf, Smooth fruit, Cylindrical fruit shape (ttFFSs) - 4/16
• Dwarf, Wrinkled fruit, Spherical fruit shape (ttffSS) - 2/16
• Dwarf, Wrinkled fruit, Cylindrical fruit shape (ttffSs) - 4/16

Now you can calculate the expected frequencies by multiplying the expected ratios by the total number of observations (506) and rounding to the nearest whole number:

• Tall, Smooth fruit, Spherical fruit shape (TTFFSS) - 1/16 * 506 = 31.6 ≈ 32
• Tall, Smooth fruit, Cylindrical fruit shape (TTFFSs) - 2/16 * 506 = 63.2 ≈ 63
• Tall, Wrinkled fruit, Spherical fruit shape (TTffSS) - 1/16 * 506 = 31.6 ≈ 32
• Tall, Wrinkled fruit, Cylindrical fruit shape (TTffSs) - 2/16 * 506 = 63.2 ≈ 63
• Dwarf, Smooth fruit, Spherical fruit shape (ttFFSS) - 2/16 * 506 = 63.2 ≈ 63
• Dwarf, Smooth fruit, Cylindrical fruit shape (ttFFSs) - 4/16 * 506 = 126.4 ≈ 126
• Dwarf, Wrinkled fruit, Spherical fruit shape (ttffSS) - 2/16 * 506 = 63.2 ≈ 63
• Dwarf, Wrinkled fruit, Cylindrical fruit shape (ttffSs) - 4/16 * 506 = 126.4 ≈ 126

Now you can plug in the values into the chi-square formula and calculate the chi-square value:

χ^2 = ((36 - 32)^2 / 32) + ((41 - 63)^2 / 63) + ((207 - 32)^2 / 32) + ((222 - 63)^2 / 63) = 6.25 + 7.84 + 1513.06 + 150.06 = 1677.21

Rounding the chi-square value to the nearest hundredth gives the answer: 1677.21.