(1) Null Hypothesis, H₀: pop mean (using eggshells)=10%=0.1;
Alternative Hypothesis, H₁: mean≠10%. 2-tailed test.
(2) significance level assumed to be 0.05 (95% confidence level).
(3) estimated variance=0.1×0.9=0.09; standard deviation=√0.09=0.3. Adjust for sample size=0.3/√100=0.03.
(3) Z=(0.2-0.1)/0.03=3.3333
(4) critical value for Z=3.3333=0.9996. Z=-3.3333, critical value is 0.0004.
For a 2-tailed test anything less than 0.025 means that we reject H₀ and by default accept H₁, implying that the fertiliser was effective.