An agricultural scientist is investigating the water efficiency of two irrigation methods: Drip Irrigation and Sprinkler Irrigation. The scientist measures the volume of water, in cubic meters per hectare (m3m^3m3), used for a specific crop across several test plots. The results for two independent random samples are summarized in the table below:
| Irrigation Method | Sample Size (nnn) | Mean (xˉ\bar{x}xˉ) | Standard Deviation (sss) |
|---|---|---|---|
| Drip (D) | 48 | 215.4 | 18.2 |
| Sprinkler (S) | 52 | 224.8 | 22.5 |
By stating your hypotheses clearly, test at the 5% significance level whether there is evidence of a difference in the mean water consumption between the two irrigation methods.
A separate meta-analysis of historical irrigation data is later reviewed. In this analysis, while the Drip method again showed lower consumption, the calculated test statistic for the difference in means was found to be z=−1.42z = -1.42z=−1.42.
A local farmer claims that the Drip method is specifically more efficient, meaning it uses a lower average volume of water than the Sprinkler method.
Test the farmer's claim using the test statistic from the meta-analysis (z=−1.42z = -1.42z=−1.42), stating the hypotheses and the critical value you would use. Conduct this test at the 5% level of significance.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.