Agriculturalists investigating a poorly growing onion crop discovered it was infected with a fungal pathogen. The fungus secreted a lectin-like protein in the soil surrounding the onions’ roots. Lectins often accelerate mitosis in root systems, but this abnormal growth creates weaker plant tissues. Fifty cell samples were observed for the struggling onion crop. The observed number of cells in each part of the cell cycle are shown below: Interphase Mitosis

Sample One 21 29

Sample Two 18 32

Sample Three 25 25

a) State the null and alternative hypothesis related to the data.

b) Calculate the chi-square values for interphase and mitosis using the samples as the observed values (o) and trial 1 in table 3 as your expected data (e).

c) Using the chi-square table, determine the critical value for interphase and mitosis of the struggling onion crop using the chi-square values in (b).

p-

value Degrees of Freedom

1 2 3 4 5 6 7 8

0.05 3.84 5.99 7.82 9.49 11.07 12.59 14.07 15.11

0.01 6.64 9.21 11.34 13.28 15.09 16.81 18.48 20.09

d) Based on the chi-square and critical value, draw a conclusion about the null hypothesis.

To answer this question, researchers studied populations of the dusky salamander (desmognathus ochrophaeus) living on different mountain ranges in the southern appalachian mountains. the researchers tested the reproductive isolation of pairs of salamander populations by leaving one male and one female together and later checking the females for the presence of sperm. four mating combinations were tested for each pair of populations (a and b)—two within the same population (female a with male a and female b with male b) and two between populations (female a with male b and female b with male a). the proportion of successful matings for each mating combination was measured. for example, when all the matings of a particular combination were successful, the researchers gave it a value of 1; when none of the matings were successful, they gave it a value of 0. then the researchers calculated an index of reproductive isolation that ranged from 0 (no isolation) to 2 (full isolation). the reproductive isolation value for two populations is the sum of the proportion of successful matings of each type within populations (aa + bb) minus the sum of the proportion of successful matings of each type between populations (ab + ba). the table provides data for the geographic distances and reproductive isolation values for 27 pairs of dusky salamander populations.