Astudy of the pay of corporate chief executive officers (ceos) examined the increase in cash compensation of the ceos of 104 companies, adjusted for inflation, in a recent year. the mean increase in real compensation was x¯ = 6.9%, and the standard deviation of the increases was s = 55%. is this good evidence that the mean real compensation µ of all ceos increased that year? the hypotheses are

h0: %u03bc = 0 (no increase) ha: %u03bc > 0 (an increase)

because the sample size is large, the sample s is close to the population %u03c3 , so take %u03c3 = 55%.

(a) sketch the normal curve for the sampling distribution of x when h0 is true. shade the area that represents thep-value for the observed outcome x = 6.9%.

(b) calculate the p -value.