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)

H0: chromosome damage during surgery evenly distributed among three cell categories.

H1: chromosome damage during surgery is not evenly distributed among three cell categories.

b)

Total number of damaged chromosome = 128 + 166 + 168 = 462

If they are evenly distributed among three cell categories then expected number of chromosome in each category = 462 * 1/3 = 154

i)

Expected frequenct table

TYPE I	TYPE II	TYPE III
154	154	154

ii)

Based on a visual comparison between the actual sample and the expected values,I think that they are not evenly distributed among the three categories of cells. The observed frequency for type I chromosome is very less ,128, compared to 154

c)

i)

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

ii)

Let level of significance be 0.05 i.e. probability of type 1 error is 5 %.

Based on the P-value < 0.05 , so reject null hypothesis, chromosome damage is not evenly distributed among the three categories of cells.

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