. A test for SARS-Cov-2 has sensitivity of 0.8 and specificity of 0.7. a. A person tested positive in the test, what is the probability that they have the virus? b. A person tested negative in the test, what is the probability that they have the virus?
1. A test for SARS-Cov-2 has sensitivity of 0.8 and specificity of 0.7.
a. A person tested positive in the test, what is the
b. A person tested negative in the test, what is the probability that they have the virus?
2. Two species of fish have similar phenotypes to each other, researchers wonder if they can classify
these fish species based on their sizes. One species has mean size of 10cm, with standard deviation of 1. The
other species has mean size of 12cm, with standard deviation of 2. Size of 15 fish from each species were
measured.
a. Which hypothesis testing method can be used to compare the mean size of the two populations? Perform
the test for α = 0.01. How does result of this test help the researchers to decide if they can classify these fish
species based on their sizes?
b. What is the power of the test? How does power of the test help the researchers to decide if they can classify
these fish species based on their sizes?
3. A shopkeeper wonders if number of their female and male customers are equal or not. They count the
customers of each gender for a day, they find that 48 females and 53 males visit the shop. Make a hypothesis test
to decide if number of females and males are significantly different from each other or not. Report a p-value for
significance.
4. A researcher wonders if expression levels of genes and proteins are highly correlated or not. They
measure expression levels of 10 genes and the proteins encoded by them. Then, Pearson
calculated to be 0.75. Conduct a hypothesis test to decide if correlation of gene and protein expression is more
than 0.4. Use α = 0.05.
5. A researcher measures expression levels of 20000 genes for ‘no treatment’ case and ‘drug treatment’
case in a cell line, experiment was made in 4 replicates. The researcher asks for your help in:
a. How to compare expression level of each gene in no treatment and drug treatment cases statistically? Which
hypothesis test methods can be used?
b. The researcher would like to correct the p-values for multiple hypothesis testing. The drug is used in high
dose, so it should change expression levels of some genes. Which multiple hypothesis testing correction
method is best in this case?
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