SAMPLE STATISTICS: mean sitting height (x bar)=92.8cm, size (n)=36 male students.
POPULATION STATISTIC: mean sitting height (µ)=91.4cm, standard deviation (σ)=3.6cm.
CLAIM: Mean sitting height is different from 91.4cm.
COUNTERCLAIM: Mean sitting height is 91.4cm.
SIGNIFICANCE LEVEL: ɑ=0.05 (95% confidence level)
Null hypothesis, H₀: µ=91.4 (counterclaim)
Alternative hypothesis, H₁: µ≠91.4 (claim)
This is a 2-tail test, because “not equals” means less than (left tail) or greater than (right tail), so the significance level is split equally between the two tails giving us the required confidence interval of 95%.
Z=(x bar-µ)/(σ/√n)=(92.8-91.4)/(3.6/√36)=1.4/0.6=2.333, corresponding to a P-value of 0.0098. The given test statistic is 0.0198.
ɑ/2=0.025 and sample P-value 0.0098<0.025, and 0.0198<0.025, which means that H₀ is rejected, and H₁ is accepted to be true. The conclusion is that the claim is true, that the mean sitting height of male students is different from 91.4cm.