Sampling - Estimating a Population

A café asks a sample of 25 customers which cake they would choose.

9 choose lemon, 11 choose chocolate and 5 choose carrot.

The café expects to sell 400 cakes next week.

Work out how many lemon cakes the café should make.

Asha asks 40 of the 720 students at a college whether they have a part-time job.

13 of the students she asks have a part-time job.

Work out an estimate for the number of the 720 students who do not have a part-time job.

In a random sample of 40 households, 14 have a dog. What percentage of the households in the sample have a dog?

A sports club has 630 members.

In a sample of 45 members, 12 want a new club kit.

Which calculation gives an estimate for the number of the 630 members who want a new club kit?

1. \frac{45}{12}\times630
2. 630-45+12
3. \frac{12}{45}\times630
4. \frac{12}{630}\times45

Two clubs each draw a pie chart to show their members' favourite sport.

In Club A's pie chart, the angle for tennis is 100^\circ.

In Club B's pie chart, the angle for tennis is 80^\circ.

Ola says, "More members of Club A chose tennis than members of Club B."

Is Ola right?

1. Yes, because 100^\circ is bigger than 80^\circ
2. No, because Club B's angle for tennis is smaller
3. Not necessarily: a pie chart shows proportions, not numbers, and we do not know how many members each club has
4. Yes, because a pie chart always shows the number of people

Mia asks 50 people which fruit they like best. 19 of them choose apples.

Jack asks 90 people which fruit they like best. He draws a pie chart of his results. The angle for apples is 108^\circ.

What fraction of the people in Jack's survey chose apples? Give your answer in its simplest form.

In whose survey did a greater proportion of people choose apples?

1. Mia's
2. Jack's
3. The proportion is the same in both surveys

A random sample of 60 members chooses an activity. The club has 450 members. Use the sample to estimate how many members would choose walking.

Hana spins a spinner 10 times. It lands on red 7 times.

Ian spins the same spinner 90 times. It lands on red 45 times.

Gus says, "Hana's results give 0.7 and Ian's give 0.5, so the best estimate for the probability of red is the mean of these, 0.6"

Use all of the results to work out a better estimate for the probability that the spinner lands on red. Give your answer as a decimal.

Why is Gus wrong?

1. Ian spun the spinner more times, so his results should count for more than Hana's
2. The mean of two probabilities is always more than 1
3. Hana's results should count for more, because she got more reds
4. Probabilities can never be added together

Two random samples are used to estimate support for a new sports centre. Sample A has 24 supporters out of 40 people. Sample B has 33 supporters out of 60 people.

What percentage of sample A supports the centre?

What percentage of sample B supports the centre?

Which sample has the greater proportion of supporters?

1. A
2. B
3. They are equal

In a sample of 50 customers, 18 prefer a morning delivery. The business has 600 customers.

Estimate how many customers prefer a morning delivery.

Which assumption supports this estimate?

1. The sample’s preferences are representative of all customers
2. Every customer must prefer mornings
3. The sample contains 600 customers

A sports centre expects 2400 people at a swimming gala.

The manager asks a sample of 80 of these people what they will buy at the café.

30 say a hot drink, 18 say a cold drink and 32 say they will not buy a drink.

Work out an estimate for how many more of the 2400 people will buy a hot drink than a cold drink.

Which of these is an assumption the manager makes, with how it could affect the answer to part (a)?

1. The sample is too small, so the answer to part (a) must be too low
2. The 80 people asked are representative of all the people at the gala; if they are not, the answer to part (a) could be too high or too low
3. The manager divided 2400 by 80, so the answer to part (a) is exact
4. Hot drinks are nicer than cold drinks, so more people will buy them

Two cafés ask some of their customers whether they would like oat milk.

At Café A, 18 customers say yes and 27 say no.

At Café B, 21 customers say yes and 39 say no.

What percentage of the customers asked at Café A said yes?

What percentage of the customers asked at Café B said yes?

Tom says, "Oat milk is more popular with Café B's customers, because more of them said yes." Is Tom right?

1. Yes, because 21 is more than 18
2. No, because a greater proportion said yes at Café A
3. No, because fewer customers were asked at Café B
4. Yes, because Café B asked more customers

A school surveys random samples from two year groups. Use the results to estimate the total number of pupils in these two years who travel by bus.

A shop asks 80 randomly selected customers about a new product. Of these, 28 say they would buy it. The shop expects 1200 customers next week.

Use the survey to estimate the number who would buy the product.

Sam works out 1200÷28×80 for part (a). Why is Sam’s method wrong?

1. It uses the sample fraction the wrong way round and predicts more buyers than customers
2. It gives a fraction, so it must be wrong
3. A prediction always equals the sample size

There are 3200 households in a town.

Ali and Bea want to find out how many of these households have solar panels.

Ali asks 40 households chosen at random. 9 of them have solar panels.

Bea asks 160 households chosen at random. 41 of them have solar panels.

Ali uses only his results and gets an estimate of 720 households. Bea uses only her results and gets an estimate of 820 households. Whose estimate is likely to be more reliable?

1. Ali's, because his estimate is smaller
2. Bea's, because her estimate is bigger
3. Bea's, because she asked more households than Ali
4. Both are equally reliable, because both chose households at random

Use all of the results to work out an estimate for the number of the 3200 households that have solar panels.