calls <- readxl::read_excel("state-data.xlsx", sheet = "calls") attach(calls) ## graphical summary boxplot(duration) ## checking for normality shapiro.test(duration) ## left-tailed and two-tailed sign test - by hand calls.stat <- sum(duration > 5) calls.n <- length(duration) # left-tailed p-value 1 - pbinom(calls.n - calls.stat - 1, size = calls.n, prob = 1/2) # two-tailed p-value 2*(1 - pbinom(max(calls.stat, calls.n - calls.stat) - 1, size = calls.n, prob = 1/2)) ## direct solution binom.test(calls.stat, n = calls.n, p = 1/2, alternative = "less") binom.test(calls.stat, n = calls.n, p = 1/2)