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## Main Question or Discussion Point

How is hypothesis testing performed for multivariate data?

Say for simplicity we have two iid draws from a binomial distribution Bin(10,q) with X1=7, X2=8. Under the null hypothesis H0:q=1/2, the individual p-values (as one-tail probabilities) are approximately 0.172 and 0.055 respectively so neither data point is sufficient evidence on its own to reject the null at the 95% confidence level. What would be the p-value for the pair (7,8) ?

Say for simplicity we have two iid draws from a binomial distribution Bin(10,q) with X1=7, X2=8. Under the null hypothesis H0:q=1/2, the individual p-values (as one-tail probabilities) are approximately 0.172 and 0.055 respectively so neither data point is sufficient evidence on its own to reject the null at the 95% confidence level. What would be the p-value for the pair (7,8) ?