10) If we conduct a single, one-sided hypothesis test, we can write down the p-value associated with it as p = P {T > tobs}, Where T is a test statistic and tobs is the observed value of that test statistic for a single set of data. Suppose that instead of conducting a single hypothesis test, we collect many independent data sets, repeat the test by computing a pvalue in each one, and analyze the distribution of those p-values. In this context, the pvalue is a random variable and we can write it as function of the samples of observed data, i.6. PV = P{T > tobs I Tobs = tobs}. a) (2pts) If the null hypothesis is true, _ show that the distribution of a random pvalue, PV, has a uniform distribution on [0,1] by calculating its cumulative distribution function. You can assume that the CDF of the test statistic T, denoted as FT(t) admits an inverse everywhere, F;1(p). b) (3pts) If 200 pvalues are collected under the same experimental conditions and 4 are highly signicant (less than 0.01), 13 are signicant (between 0.01 and 0.05) and the remainder are above 0.05, conduct a goodnessoft test that the null hypothesis is true and the pvalues come from a uniform distribution