The fill mass X X\,X g of a product is Normally distributed with known standard deviation 6 g. A researcher tests H0:μ=50H_0:\mu=50H0:μ=50 against H1:μ>50H_1:\mu>50H1:μ>50, where μ \mu\,μ is the population mean fill mass in grams, using a random sample of size 36.
Find the critical region for Xˉ \bar X\,Xˉ at the 5% significance level.
A sample gives xˉ=51.7\bar x=51.7xˉ=51.7. Carry out the test and interpret the result in context.