7 A physiotherapist is investigating hand grip strength in adult women under 30 years old. She thinks that the grip strength of the dominant hand will be on average 2 kg higher than the grip strength of the non-dominant hand.
The physiotherapist selects a random sample of 12 adult women under 30 years old and measures the grip strength of each of their hands. She then uses software to produce a \(95 \%\) confidence interval for the mean difference in grip strength between the two hands (dominant minus nondominant), as shown in Fig. 7.
\begin{table}[h]
| T Estimate of a Mean |
| Confidence Level | 0.95 |
| Sample |
\multirow{3}{*}{| } | | | | | | Result | | T Estimate of a Mean | | Mean | 2.79 | | s | 3.92 | | SE | 1.13161 | | N | 12 | | df | 11 | | Lower Limit | 0.29935 | | Upper Limit | 5.28065 | | Interval | \(2.79 \pm 2.49065\) |
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{table}
- Explain why the physiotherapist used the same people for testing their dominant and nondominant grip strengths.
- State any assumptions necessary in order to construct the confidence interval shown in Fig. 7.
- Explain whether the confidence interval supports the physiotherapist's belief.
- The physiotherapist then finds some data which have previously been collected on grip strength using a sample of 100 adult women. A 95\% confidence interval, based on this sample and calculated using a Normal distribution, for the mean difference in grip strength between the two hands (dominant minus non-dominant) is (1.94, 2.84).
- For this sample, find
- the standard deviation of the differences.
(ii) Explain what you would need to know about the nature of this sample if you wanted to draw conclusions about the mean difference in grip strength in the population of adult women.
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