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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.