The manufacturer of glo more flat white interior latex paint

The manufacturer of glo more flat white interior latex paint claims one coat coverage off 400 square feet per gallon on interior walls. A painter keeps careful track of 6 gallons and finds coverage (in square feet) of 360,410,380,360,390,400. At a=0.10 is there evidence that coverage is less than 400 square feet per gallon follow the steps for critical value approach to test the claim. What is the critical value ?

Solution

Test- H0: population mean = 400 ag. H1: population mean < 400...
mean for 6 gallons of the sample = 383.333...s.d = 20.65591..and standard error = s.d / sqrt(6) = 8.43274.....

Test statistic = ( 383.333-400 ) / 8.43274 = -1.9764...
critical value for a = 0.10 is - 2.015048...

since , -2.015048 < -1.9764...we don\'t have any evidence to reject H0... THERE IS NO EVIDENCE THAT COVERAGE IS LESS THAN 400 SQ FEET PER GALLON......