Numeracy Higher November 2016 Unit 2 Q6
6. Porth Ifan Hospital has made some changes to improve patient care.
A survey is to be used to find out the views of the hospital staff.
(a) The table shows the total number of staff in each job type.
| Job type | Doctor | Nurse | Management | Clerical |
|---|---|---|---|---|
| Number of staff | 120 | 320 | 56 | 144 |
The survey is to be given to a sample of 75 staff.
Use a stratified sampling method to calculate the number of staff from each job type that should be asked to complete the survey.
You must show your working. [4]
| Job type | Doctor | Nurse | Management | Clerical |
|---|---|---|---|---|
| Number in sample |
(b) The hospital decides to take a random sample of its 120 doctors to select those needed for the survey.
Use the following list of random numbers to select the first 5 doctors.
You must start with the first number in the list, explaining clearly how you are using the numbers to select the sample. [3]
Use the following list of random numbers to select the first 5 doctors.
You must start with the first number in the list, explaining clearly how you are using the numbers to select the sample. [3]
| 032 | 520 | 021 | 924 | 152 | 627 | 351 | 295 | 081 | 495 |
| 542 | 708 | 339 | 557 | 396 | 949 | 417 | 235 | 962 | 261 |
| 837 | 783 | 983 | 493 | 876 | 924 | 032 | 421 | 205 | 740 |
| 055 | 491 | 806 | 415 | 158 | 392 | 441 | 521 | 105 | 342 |
| 782 | 398 | 923 | 729 | 968 | 244 | 119 | 480 | 451 | 780 |
| Scheme | Marks | Comments |
|---|---|---|
| (Total =) 640 75 × (number of staff in a job type) ÷ 640 | B1 M1 | Sight of this calculation for any one job type FT ‘their total’ |
| (List of unrounded answers =) 14∙0625, 37∙5, 6∙5625, 16∙875 (Number in sample =) 14, 37, 7, 17 | A1 A1 | Allow A1 for any 2 correct CAO |
| Scheme | Marks | Comments |
|---|---|---|
| ‘Each doctor is given a 3-digit number from 001 to 120’ | B1 | Or any 120 different numbers OR Each doctor is given a number from 1 to 120, and the random numbers are then partitioned in groups of 3 |
| ‘Use the table to select numbers in the range (1 to 120), ignoring repeats’ | B1 | If they are not working in rows or columns, they need to explain how they are working (Note: the numbers have to be used one at a time) |
| (Working in rows would produce) 032, 021, 081, (Working in columns would produce) 032, 055, 021, | B1 | Alternative: B1 for ‘the 3-digit number is divided by 120 with the remainder used, a remainder of zero means that doctor 120 is chosen, ignore the numbers 000 and 961 – 999 and repeats, OR 960 – 999 ,and repeats’ B1 for (working in rows would produce) 032, 040, 021, 084, (working in columns would produce) 032, 062, 117, 055, |