- A glue supplier claims that Goglue is stronger than Tackfast. A company is presently using Tackfast but agrees to change to Goglue if, at the 5\% significance level,
- the standard deviation of the force required for Goglue to fail is not greater than the standard deviation of the force required for Tackfast to fail and
- the mean force required for Goglue to fail is more than 4 newtons greater than the mean force for Tackfast to fail.
A series of trials is carried out, using Goglue and Tackfast, and the glues are tested to destruction. The force, \(x\) newtons, at which each glue fails is recorded.
| Sample size \(( n )\) | Sample mean \(( \bar { x } )\) | Standard deviation \(( s )\) |
| Tackfast \(( T )\) | 6 | 5.27 | 0.31 |
| Goglue \(( G )\) | 5 | 10.12 | 0.66 |
It can be assumed that the force at which each glue fails is normally distributed.
- Test, at the \(5 \%\) level of significance, whether or not there is evidence that the standard deviation of the force required for Goglue to fail is greater than the standard deviation of the force required for the Tackfast to fail. State your hypotheses clearly.
The supplier claims that the mean force required for its Goglue to fail is more than 4 newtons greater than the mean force required for Tackfast to fail.
- Stating your hypotheses clearly and using a \(5 \%\) level of significance, test the supplier's claim.
- Show that, at the \(5 \%\) level of significance, the supplier's claim will be accepted if \(\bar { X } _ { G } - \bar { X } _ { T } > 4.55\), where \(\bar { X } _ { G }\) and \(\bar { X } _ { T }\) are the mean forces required for Goglue to fail and Tackfast to fail respectively.
Later, it was found that an error had been made when recording the results for Goglue. This resulted in all the forces recorded for Goglue being 0.5 newtons more than they should have been. The results for Tackfast were correct.
- Explain whether or not this information affects the decision about which glue the supplier decides to use.