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# We plan to test whether the mean mRNA expression level differs between two strains of yeast, for each of 8,000 genes. We will measure the expression levels of each gene, in n samples of strain 1 and m samples of strain 2. We plan to compute a P-value for each gene, using an unpaired two-sample t-test for each gene $the particular type of test does not matter$. a) What are the null hypotheses in these tests $in words$? [2] b) If, in fact, the two strains are identical, how many of these tests do we expect to produce a P-value exceeding 1/4? [2]

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## Answer to a math question We plan to test whether the mean mRNA expression level differs between two strains of yeast, for each of 8,000 genes. We will measure the expression levels of each gene, in n samples of strain 1 and m samples of strain 2. We plan to compute a P-value for each gene, using an unpaired two-sample t-test for each gene $the particular type of test does not matter$. a) What are the null hypotheses in these tests $in words$? [2] b) If, in fact, the two strains are identical, how many of these tests do we expect to produce a P-value exceeding 1/4? [2]

Corbin
4.6
a) The null hypothesis in these tests states that the mean mRNA expression level is the same in both strains of yeast. In other words, there is no difference in the mean expression levels between strain 1 and strain 2 for each gene.

b) If the two strains are identical, we would expect approximately 25% $1/4$ of these tests to produce a P-value exceeding 1/4. This is based on the assumption that the P-values follow a uniform distribution under the null hypothesis.

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