7 For the year 2014, the table below summarises the weights, \(x\) kilograms, of a random sample of 160 women residing in a particular city who are aged between 18 years and 25 years.
| Weight ( \(\boldsymbol { x }\) kg) | Number of women |
| 35-40 | 4 |
| 40-45 | 9 |
| 45-50 | 12 |
| 50-55 | 16 |
| 55-60 | 24 |
| 60-65 | 28 |
| 65-70 | 24 |
| 70-75 | 17 |
| 75-80 | 12 |
| 80-85 | 7 |
| 85-90 | 4 |
| 90-95 | 2 |
| 95-100 | 1 |
| Total | 160 |
- Calculate estimates of the mean and the standard deviation of these 160 weights.
- Construct a 98\% confidence interval for the mean weight of women residing in the city who are aged between 18 years and 25 years.
- Hence comment on a claim that the mean weight of women residing in the city who are aged between 18 years and 25 years has increased from that of 61.7 kg in 1965.
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[2 marks]
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