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.