4 Shellfish in the sea near nuclear power stations are regularly monitored for levels of radioactivity. On a particular occasion, the levels of caesium-137 (a radioactive isotope) in a random sample of 8 cockles, measured in becquerels per kilogram, were as follows.
\(\begin{array} { l l l l l l l l } 2.36 & 2.97 & 2.69 & 3.00 & 2.51 & 2.45 & 2.21 & 2.63 \end{array}\)
Software is used to produce a 95\% confidence interval for the level of caesium-137 in the cockles. The output from the software is shown in Fig. 4. The value for 'SE' has been deliberately omitted.
T Estimate of a Mean
Confidence Level 0.95
Sample
Mean 2.6025
s 0.2793
□
0.2793
N □ 8
Result
T Estimate of a Mean
\begin{table}[h]
| Mean | 2.6025 |
| s | 0.2793 |
| SE | |
| N | 8 |
| df | 7 |
| Interval | \(2.6025 \pm 0.2335\) |
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{table}
- State an assumption necessary for the use of the \(t\) distribution in the construction of this confidence interval.
- State the confidence interval which the software gives in the form \(a < \mu < b\).
- In the software output shown in Fig. 4, SE stands for standard error. Find the standard error in this case.
- Show how the value of 0.2335 in the confidence interval was calculated.
- State how, using this sample, a wider confidence interval could be produced.