Moderate -0.3 This is a straightforward one-sample z-test application with all information clearly provided. Students must set up hypotheses (H₀: μ = 8.2 vs H₁: μ > 8.2), calculate the test statistic z = (8.7-8.2)/(1.2/√16) = 1.667, compare to critical value 1.645, and conclude. While it requires understanding of hypothesis testing framework, it's a standard textbook exercise with no conceptual complications or multi-step reasoning—slightly easier than average due to its routine nature.
In the past, the mean annual crop yield from a particular field has been 8.2 tonnes. During the last 16 years, a new fertiliser has been used on the field. The mean yield for these 16 years is 8.7 tonnes. Assume that yields are normally distributed with standard deviation 1.2 tonnes. Carry out a test at the 5\% significance level of whether the mean yield has increased. [5]
Question 2:
2 | Ho: Pop mean yield = 8.2
H1: Pop mean yield > 8.2
(±)8.7−8.2
1.2/ 16
= (±)1.667
Comp z = 1.645 Or Area comparison
0.0475-0.0478)
Reject H
0
Evidence that mean yield has increased | B1
M1
A1
M1
A1 [5] | or µ = 8.2(not just “mean”)
µ > 8.2
Allow without √ sign (Allow cc)
Or comp 1 - Φ('1.667') with 0.05
Valid Comparison z-values (same sign) or areas
No Contradictions
No follow through for 2 tail test
In the past, the mean annual crop yield from a particular field has been 8.2 tonnes. During the last 16 years, a new fertiliser has been used on the field. The mean yield for these 16 years is 8.7 tonnes. Assume that yields are normally distributed with standard deviation 1.2 tonnes. Carry out a test at the 5\% significance level of whether the mean yield has increased. [5]
\hfill \mbox{\textit{CAIE S2 2016 Q2 [5]}}