Question

1. In an experiment using hamster ovaries, researchers want to determine if chromosome damage during surgery with H₂O₂ is not evenly distributed among three cell categories.

1. Write the hypotheses for a goodness of fit test.

2. Distribution of damaged chromosomes by cell category:

TYPE I	TYPE II	TYPE III
128	166	168

1. Find the expected values for each cell category.

TYPE I	TYPE II	TYPE III

2. Based on a visual comparison between the actual sample and the expected values, does chromosome damage seem not to be evenly distributed among the three categories of cells? Why or why not?

3. The P-value from the Goodness-of-Fit test is 0.037.
   1. Fill in the blanks: If the distribution of damage is__________ _____     among the cell categories, then there is a _____% chance of obtaining the observed values or values farther from expected.

2. Based on the P-value, is chromosome damage not evenly distributed among the three categories of cells? Why or why not?

Answer 1

a.

Null Hypothesis H0: The chromosome damage during surgery with H2O2 is evenly distributed among three cell categories.

Alternative Hypothesis Ha: The chromosome damage during surgery with H2O2 is not evenly distributed among three cell categories.

b.

N = 128 + 166 + 168 = 462

Expected values = N * p where p = 1/3 (for evenly distributed)

= 462 * (1/3) = 154

TYPE I 154

TYPE II 154

TYPE III 154

c.

Based on a visual comparison between the actual sample and the expected values, the chromosome damage does not seem to be evenly distributed as the actual and expected values are quite different.

d.

If the distribution of damage is evenly  among the cell categories, then there is a 3.7 % chance of obtaining the observed values or values farther from expected.

Since p-value is less than 0.05 significance level, we reject the null hypothesis.

Based on the P-value, We conclude that the chromosome damage is not evenly distributed among the three categories of cells because of low p-value.