SAMPLE STATISTICS: mean weight of garbage (x bar)=27.553lb, size (n)=62 households.
POPULATION STATISTIC: standard deviation (σ)=12.458lb.
CLAIM: Mean weight of garbage is less than 30lb.
COUNTERCLAIM: Mean weight of garbage is greater than or equal to 30lb.
SIGNIFICANCE LEVEL: ɑ=0.05 (95% confidence level)
Null hypothesis, H₀: µ=30 (from counterclaim, which permits µ=30)
Alternative hypothesis, H₁: µ<30 (claim)
This is a left tail test.
TEST STATISTIC: Z=(x bar-µ)/(σ/√n)=(27.553-30)/(12.458/√62)=-1.547, corresponding to a P-value of 0.061.
ɑ=0.05 and sample P-value 0.061>0.05, which means that H₀ fails to be rejected. We conclude that there is insufficient evidence to decide with 95% confidence whether or not the mean weight of garbage is less than 30lb. Although the sample weight was less than 30lb, it wasn’t significantly less.