If there was no true difference in any genotypes between the two groups how many pvalues would you expect to see < 0.05

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In a single rmarkdown file answer the following questions:

Two groups of people have volunteered to take part in a genetic study. Group 1 (n = 126) are volunteers with no history of Type I Diabetes in their immediate family, whilst Group 2 (n = 183) have all been diagnosed with Type I Diabetes. A genotyping study was undertaken on these volunteers using 25,786 SNPs selected due to their proximity to key immune genes. Researchers are looking to identify any SNP genotypes which may increase the risk of Type I Diabetes. In your answer, consider the reference SNP allele as A and the alternate SNP allele as B , using the genotypes AA , AB and BB .

a. For an individual SNP, what test would be appropriate for this comparison? 

b. Define H₀ and Hₐ for the genotype at each individual SNP. 

c. If there was no true difference in any genotypes between the two groups, how many pvalues would you expect to see < 0.05? 

d. Using Bonferroni’s method, what would a suitable cutoff value be to consider an SNP as being associated with an increased risk of Type I diabetes, i.e., to reject H₀ [1 mark]

e. Given the following genotype table, would you reject or fail to reject H₀? Provide your work and a full explanation. 

Group       AA    AB     BB

Control     25     60     41

T1D          21     55    103

An experiment was repeated multiple times, in which GFP fluorescence was measured in a cell culture as a measurement of gene expression, both before and after viral transfection. GFP was present on a plasmid as a reporter for activity at a specific promoter. The change in fluorescence values obtained for each repeat are given below as the vector x, presented on the log2 scale for your individual subset of experiments.

a. Define H₀ and Hₐ 

b. Calculate the sample mean and sample variance in R

c. Calculate the T-statistic using R .

d. What would the degrees of freedom be for your t-test?

e. Calculate the p-value using R 

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