6 The label on a pack of strawberries in a large batch states that it holds 250 g of strawberries. A random sample of 40 packs from the batch is selected and software is used to produce a \(95 \%\) confidence interval for the mean weight of strawberries per pack. An extract from the software output is shown in Fig. 6.
\begin{table}[h]
| Sample Mean | 248.92 |
| Standard Error | 0.61506 |
| Sample Size | 40 |
| Confidence Level | 0.95 |
| Interval | \(248.92 \pm 1.2055\) |
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{table}
- Explain whether the confidence interval suggests that the mean weight of strawberries per pack in the batch is different from 250 g .
- A manager looking at the data says that the conclusion would have been different if a \(90 \%\) confidence interval had been used.
Determine whether the manager is correct. - Explain briefly whether or not it is appropriate for the manager to vary the confidence level before coming to any conclusions.
[0pt] - On another occasion, using the same sample size, a 95\% confidence interval for the mean weight of strawberries per pack is [248.05, 249.95].
Find the sample variance in this case. - Explain the meaning of a 95\% confidence interval.