Sampling methods

A maths teacher holds a revision session every Wednesday.

In a random sample of eight Wednesdays, the number of students who attended is listed below.

2 4 3 1 4 5 2 3

Find the mean of these eight values.

Find the variance of these eight values.

The teacher believes that the number of students who attended a revision session each Wednesday can be modelled by the binomial distribution B(30, 0.1).

Comment on whether the mean and variance found in parts (a) and (b) support the teacher’s belief.

Fully justify your answer.

The teacher wanted to decide if a Saturday morning revision session was worth doing.

The teacher asked the first 10 students who entered the classroom if they would attend a Saturday session.

Name this method of sampling.

Describe one advantage of this method of sampling.

A random sample of eight cars was selected from the Large Data Set.

The masses of these cars, in kilograms, were as follows.

950 989 1247 1415 1506 1680 1833 2040

It is given that, for the population of cars in the Large Data Set:

It was decided to remove any of the masses which fall outside the following interval.

median 15 interquartile range mass median 15 interquartile range

Show that only one of the eight masses in the sample should be removed.

Write down the statistical name for the mass that should be removed in part (a)(i).

The table shows the probability distribution of the number of previous owners, N, for a sample of cars taken from the Large Data Set.

	0	1	2	3	4	5	6 or more
P( = )	0.14	0.37	0.9k	0.25	0.4k	1.7k	0

An expert team is investigating whether there have been any changes in CO₂ emissions from all cars taken from the Large Data Set.

The team decided to collect a quota sample of 200 cars to reflect the different years and the different makes of cars in the Large Data Set.

Using your knowledge of the Large Data Set, explain how the team can collect this sample.

Describe one disadvantage of quota sampling.

Researchers are investigating the average time spent on social media by adults on the electoral register of a town.

They select every 100th adult from the electoral register for their investigation.

Identify the population in their investigation.

State the name of this method of sampling.

Describe one advantage of this sampling method.

An electoral register contains 8000 names.

A researcher decides to select a systematic sample of 100 names from the register.

Explain how the researcher should select such a sample.

A political party is holding an election to choose a new leader.

A statistician within the party decides to sample 70 party members to find their opinions of the leadership candidates.

There are 4735 members under 30 years old and 8565 members 30 years old and over.

The statistician wants to use a sample of 70 party members in the survey.

He decides to use a random stratified sample.

Calculate how many of each age group should be included in his sample.

Explain how he could collect the random sample of members under 30 years old.

Lenny is one of a team of people interviewing shoppers in a town centre.

He is asked to survey 50 women between the ages of 18 and 29

Identify the name of this type of sampling.

Circle your answer.

simple random stratified quota systematic

In a region of England, the government decides to use an advertising campaign to encourage people to eat more healthily.

Before the campaign, the mean consumption of chocolate per person per week was known to be 66.5 g, with a standard deviation of 21.2 g

After the campaign, the first 750 available people from this region were surveyed to find out their average consumption of chocolate.

State the sampling method used to collect the survey.

Explain why this sample should not be used to conduct a hypothesis test.

A second sample of 750 people revealed that the mean consumption of chocolate per person per week was 65.4 g

Investigate, at the 10% level of significance, whether the advertising campaign has decreased the mean consumption of chocolate per person per week.

Assume that an appropriate sampling method was used and that the consumption of chocolate is normally distributed with an unchanged standard deviation.