Question

A sample of 62 households were is taking to measure the amount of discarded plastics. the sample mean was 1.911 lbs and the standard deviation was 1.065lbs. test the hypothesis that the amount of discarded plastics per household was different from the population mean 1.800lbs. at significance level 0.10

Answer 1

Ho : mu = 1.80 lbs
Ha : mu != 1.80 lbs

Level of Significance (l.o.s.) : alpha = 0.10

Decision Criteria : Reject Ho at 10% l.o.s. if t cal > t tab,
where t tab = t( alpha/2 , n-1 ) = t(0.05 , 61 ) = 1.67022

Calculations : n = 62, x(bar) = 1.911 lbs and s = 1.065 lbs

t cal = [ x(bar) - mu ] / [ s / sqrt(n) ]
= [ 1.911 - 1.80 ] / [ 1.065 / sqrt(62) ]
= 0.82067

Conclusion : Since t cal < t tab, we do not reject Ho at 10% l.o.s. and thus, conclude that the population mean is 1.800lbs

Hope this answers your query!