October 2021 Paper 2 Q10
10 A researcher plans to carry out a statistical investigation to test whether there is linear correlation between the time (\(T\) weeks) from conception to birth, and the birth weight (\(W\) grams) of new-born babies.
The researcher records the values of \(T\) and \(W\) for a random sample of 11 babies. They calculate Pearson’s product-moment correlation coefficient for the sample and find that the value is 0.722.
Critical values of Pearson’s product-moment correlation coefficient.
| 1-tail test | 5% | 2.5% | 1% | 0.5% | |
| 2-tail test | 10% | 5% | 2.5% | 1% | |
| \(n\) | 10 | 0.5494 | 0.6319 | 0.7155 | 0.7646 |
| 11 | 0.5214 | 0.6021 | 0.6851 | 0.7348 | |
| 12 | 0.4973 | 0.5760 | 0.6581 | 0.7079 | |
| 13 | 0.4762 | 0.5529 | 0.6339 | 0.6835 |
| Scheme | Marks |
|---|---|
| Very likely weight will increase with time oe or He is only looking for positive correlation | B1 |
| [1] |
Notes
Or eg "Expect weight to increase with time" oe
"Foetuses grow" oe
Ignore all else
| Scheme | Marks |
|---|---|
| \(\mathrm{H}_0: \rho = 0\) Allow other letters | B1 |
| \(\mathrm{H}_1: \rho \gt 0\) where \(\rho\) is the correlation coefficient for the population or where \(\rho\) is the correlation coefficient between time and weight | B1 |
| Comp 0.722 with 0.6851 | M1 |
| Reject \(\mathrm{H}_0\). Condone Accept \(\mathrm{H}_1\) | M1 |
| There is evidence of (positive linear) correlation between time from conception to birth and weight of new-born babies Or eg It appears that birth weight increases with time (from conception to birth) | A1 |
| [5] |
Notes
B1B0 for 1 error, eg undefined \(\rho\) or 2-tail
For hypotheses in words, not using parameter:
\(\mathrm{H}_0\): There is no correlation between time and weight
\(\mathrm{H}_1\): There is positive correlation between time and weight B1B0
But omission of “positive”: B0B0
M1: May be implied by conclusion
A1: Allow without "positive” and without “linear"
In context, not definite