June 2022 Paper 2 Q13
13 Records from the 1950s showed that 35% of human babies were born without wisdom teeth. It is believed that as part of the evolutionary process more babies are now born without wisdom teeth. In a random sample of 140 babies, collected in 2020, a researcher found that 61 were born without wisdom teeth.
The researcher made the following statement.
“This shows that the percentage of babies born without wisdom teeth has increased from 35%.”
| Scheme | Marks | AO |
|---|---|---|
| it can’t be fully justified because eg different samples may lead to different conclusions oe eg the proportion could be 0.35 and 61/140 may have arisen by chance oe eg the sample may not be representative oe eg the researcher used a sample not a population oe | B1 | 2.4 |
| [1] |
Notes
B1: do not allow
eg the sample is too small
eg the sample is too small to be representative
| Scheme | Marks | AO |
|---|---|---|
| \(\mathrm{H_0}: p = 0.35\) \(\mathrm{H_1}: p \gt 0.35\) | B1 | 1.1 |
| \(p\) is the probability that a baby (selected at random) is born without wisdom teeth | B1 | 2.5 |
| \(\mathrm{P}(X \geqslant k)\) found using \(\mathrm{B}(140, 0.35)\), where \(k = 60\), 61 or 62 NB \(\mathrm{P}(X \geqslant 60) = 0.03272 - 0.033\) or \(\mathrm{P}(X \geqslant 62) = 0.01438 - 0.015\) NB 0.967…, 0.978… and 0.985…imply M1 | M1* | 3.3 |
| \(\mathrm{P}(X \geqslant 61) = 0.02197 - 0.022\) | A1 | 1.1 |
| their 0.022 correctly compared with 0.05 | M1dep* | 3.4 |
| do not accept \(\mathrm{H_0}\) or reject \(\mathrm{H_0}\) or accept \(\mathrm{H_1}\) or significant | A1FT | 1.1 |
| sufficient evidence at the 5% level to suggest that the probability that a baby is born without wisdom teeth is more than 0.35 | A1 | 1.1 |
| [7] |
Notes
B1: allow equivalent in words;
do not allow percentages
B1: or \(p\) is the proportion of babies that are born without wisdom teeth
B1B1 if other symbol instead of \(p\) used if correctly defined
M1*: or critical region is \(X \geqslant k\) found from calculation of probability; allow \(k = 58\), 59 or 60
A1: or critical region is \(X \geqslant 59\) from 0.0475…. or 0.048
M1dep*: or 61 correctly compared with their 59;
allow their 0.978 correctly compared with 0.95
A1FT: A0 if their \(0.022 \gt 0.05\) or \(61 \lt\) their 59
A1: dependent on award of all other marks apart from second B1
do not allow eg conclude / prove / indicate or other assertive statement instead of suggest