The median of a continuous distribution for a variable X is

The median of a continuous distribution for a variable X is the value ht for which P(X > M) = .5. A scientist studying weight gain in pigs under certain conditions decides to do a test on the median weight gain, rather than the mean. He believes that the median weight gain will be 6 lbs. He takes a sample of 20 pigs and records their weight gains. 2.4 2.6 2.7 3.1 3.2 3.5 3.8 4.4 5.2 5.3 5.8 5.9 6.1 6.4 6.5 6.57.3 8.2 8.68.7 The test statistic will simply be W, which is the number of observations which are greater than 6. What is the value of that test statistic for these data?

Solution

w = no. of observations which are greater than 6...

= 10...