9 A company supplies computers to businesses. In the past the company has found that computers are kept by businesses for a mean time of 5 years before being replaced. Claud, the manager of the company, thinks that the mean time before replacing computers is now different.
- Describe how Claud could obtain a cluster sample of 120 computers used by businesses the company supplies.
Claud decides to conduct a hypothesis test at the \(5 \%\) level to test whether there is evidence to suggest that the mean time that businesses keep computers is not 5 years. He takes a random sample of 120 computers. Summary statistics for the length of time computers in this sample are kept are shown in Fig. 9.
\begin{table}[h]
| Statistics |
| \(n\) | 120 |
| Mean | 4.8855 |
| \(\sigma\) | 2.6941 |
| \(s\) | 2.7054 |
| \(\Sigma x\) | 586.2566 |
| \(\Sigma x ^ { 2 }\) | 3735.1475 |
| Min | 0.1213 |
| Q1 | 2.5472 |
| Median | 4.8692 |
| Q3 | 7.0349 |
| Max | 9.9856 |
\captionsetup{labelformat=empty}
\caption{Fig. 9}
- State the hypotheses for this test, explaining why the alternative hypothesis takes the form it does.
- Use a suitable distribution to carry out the test.