Sampling data - Intermediate test questions - GCSE Maths Numeracy (WJEC) Revision

1

Angharad wants to test the following hypotheses:

1) People on her street prefer action films to horror films.

2) Most of her friends are older than her.

3) More people in the UK have visited Cardiff than Edinburgh.

Which of the hypotheses would require sampling to test?

1 and 3

3 only

1 and 2

2

Jon decided to take a systematic sample of 25 people from a population of 150. Which interval should he use?

3

Bethan wishes to take a systematic sample of eight from a population of 48. Which of the following would form an acceptable sample?

8, 16, 24, 32, 40, 48

1, 9, 15, 21, 27, 33, 38, 43, 48

6, 12, 18, 24, 30, 36, 42, 48

4

Marc wants to select a random sample of 12 customers to his shop in order to carry out some market research. Which would be a correct way to select a random sample?

Select the first 12 customers who have visited the shop that day that have surnames beginning with a random letter

Picking the 12 people who spent the most money at the shop

Pick names of customers who have attended the shop that day from a hat

5

Craig wants to take a random sample of seven from a population of 60. He uses a random number generator to produce the following numbers:

018 641 820 936 418 745 016 237 351 734 671 820 365 187 635 012

What numbers will he select for his sample?

1, 9, 36, 41, 82, 86, 87

1, 1, 9, 36, 41, 41, 45

1, 9, 35, 36, 37 41, 45

6

Josh wants to find out what students in his school think about plans to shorten the length of the school day. He decides to take a stratified sample of 40 from the following data.

How many students should he select from each year group?

Two column table of 'Year group' and 'Number of Students'

Six from year 7, seven from Year 8, five from Year 9, 11 from Year 10, 11 from Year 11

Eight from each group

12 from Year 7, 14 from Year 8, 10 from Year 9, 22 from Year 10, 22 from Year 11

7

Amina wants to find out how likely people are to buy her new magazine. She decides to take a stratified sample from a population of 300. She uses the following table:

Two column table of 'Age group' and 'Number'

She calculates that she needs to select 8 people from the 16-25s, 24 from the 26-35s and 4 from the 36-45s. How many would she need to select from the 46-55s?

8

Michelle plans to start a new cleaning business. She decides to take a stratified sample to find out how much people are willing to pay for this service. What factor would be most important to take into account when constructing a stratified sample of people for this purpose?

Number of children

Month of birth

Hair colour

9

A survey was carried out to see how many people owned a smartphone. The information from the study is summarised in the table.

Use this data to estimate how many people you would expect to own a smartphone from a population of 6,000.

Two column table of 'Owns a smartphone' and 'Does not own a smartphone'

2,140

4,280

3,090

10

Millie wants to survey 25 athletes about their views towards sports. Of 100 athletes, 54 are male and 46 are female. She calculates that she needs to ask 14 males and 12 females.

She realises that this would be 26 people. What has gone wrong here?

She has miscalculated – she needs to check her method

The stratified sampling method does not work for this sample size

She has made a rounding error - she needs to check her calculations