An agricultural scientist is investigating whether vacuum-sealing organic blueberries extends their shelf-life compared to standard ventilated containers. The shelf-life, T T\,T days, was recorded for two independent random samples.
A random sample of 80 containers using standard ventilated packaging, and an independent random sample of 60 containers using vacuum-sealed packaging, were monitored. The results are summarized in the table below:
| Sample Group | Sample size (nnn) | ∑T\sum T∑T | ∑T2\sum T^2∑T2 | Unbiased estimate of mean | Unbiased estimate of variance |
|---|---|---|---|---|---|
| Standard | 80 | 960 | 12400 | Tˉ\bar{T}Tˉ | s2s^2s2 |
| Vacuum-sealed | 60 | - | - | 13.5 | 14.2 |
Find the values of Tˉ\bar{T}Tˉ and s2 s^2\,s2 for the standard ventilated packaging.
Test, at the 1% level of significance, whether there is evidence that the mean shelf-life of the blueberries is greater when vacuum-sealed. State your hypotheses clearly.
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.