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.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.