Identify the test

Question 1

Olivia notices that her students are worse than previous students she has taught. Experience has shown that scores obtained in a particular test are normally distributed with mean score 70 and variance 36. When the test is taken by a random sample of 36 students, the mean score is 68.5. A test for whether these students have not performed as well as expected is carried out.

Answer 1

One Sample z-test

large sample (known population variance)

Question 2

Orla times her 100 m sprint times and assumes they follow a normal distribution. She trains intensively for a week and then runs 100 m on each of 5 consecutive days. A test is carried out to see whether the training has improved her times.

Answer 2

One sample t-test

small sample, unknown population variance

Question 3

Total Nutrition are investigating the effects of adding certain vitamins to a diet. 64 two-week old rats were given a vitamin supplement in their diet for a period of one month, after which time their masses were noted. A control group of 36 rats of the same age were fed on an ordinary diet and their masses were also noted after one month. A test is carried out to see if the experimental group have a greater mass than the control group.

Answer 3

Two sample z-test

Often called difference of two means, z-test. Large samples

Question 4

Brighton politicians are conducting a public opinion poll where 1000 randomly chosen electors were asked whether they would vote for the Green Party again at the next election. The Green party believe that 40% of electors would vote for them. A test is carried out to see whether they are overestimating their support.

Answer 4

One sample binomial proportion

Question 5

Tesco purchase batches of Golden Delicious apples and test for bruising before resale. A random sample of 1000 apples contained 30 which were bruised. A second random sample of 2000 apples contained 78 bruised apples. A test is carried out to determine whether the proportions differ between the samples.

Answer 5

Two sample binomial proportions

Often known as difference of two proportions

Question 6

Will randomly selects his journey times to work and back. He records his journey times over the course of 8 randomly selected mornings and 10 randomly selected evenings and tests whether there is a difference between his morning and evening commutes. He assumes the distributions of journey times are not normally distributed.

Answer 6

Wilcoxon rank sum

Non-parametric, independent samples

Question 7

Steve thinks his students are better than previous students he has taught. Experience has shown that scores obtained in a particular test have average score 70, with a skewed distribution. The test is taken by a random sample of 16 students. A test for whether these students have performed better than expected is carried out.

Answer 7

Sign test

Non-parametric, one sample, not symmetrical

Question 8

Organic nylon is tested for quality by sampling 35 from a large batch and their tensile strength is recorded. The tensile strength of synthetic nylon is 12 400 PSI. A test is carried out to see whether organic nylon is less strong than synthetic nylon.

Answer 8

One sample z-test

large sample, uses CLT

Question 9

Simon thinks his times for running the 1500 m race follow a skewed distribution. He trains intensively for a week and then runs 1500 m on each of 5 consecutive days. A test is carried out to see whether the training has improved his times.

Answer 9

Sign test

Non-parametric, one sample, not symmetrical

Question 10

Omar notices his times for running the 100 m race follow a normal distribution with variance 14.2. He trains intensively for a week and then runs 100 m on each of 10 consecutive days. A test is carried out to see whether the training has improved his times.

Answer 10

One sample z-test

small sample from normally distributed population with known variance

Question 11

When Sam runs a 100 m race, he finds his times follow a symmetrical distribution. He trains intensively for a week and then runs 100 m on each of 10 consecutive days. A test is carried out to see whether the training has improved their times.

Answer 11

Wilcoxon signed-rank

Non-parametric, one sample, symmetrical

Question 12

Ollie and June notice that certain vitamins may affect the mass of rats. An investigation was carried out to assess the effects of adding certain vitamins to the diet. Three groups were set up: a group of 10 rats received a vitamin supplement for 2 months; a group of 8 rats received a vitamin supplement for 1 month and the usual diet for 1 month; a group of 9 rats received the usual diet for 2 months. A test is carried out to see if there is a difference in masses between the groups.

Answer 12

One-factor ANOVA

More than two categories - one factor (diet)

Question 13

Greengrocers find produce can sometimes be defective. Samples of size 5 are selected regularly from large batches and tested. During one week 500 samples are taken and the number of defective items in each sample recorded. A test to determine whether a Binomial distribution is a suitable model is carried out.

Answer 13

Goodness of fit

Test for suitability of a model - Binomial

Question 14

Peter thinks the reaction times are affected by how much fluid is consumed in the day. A sample of 15 volunteers are asked to participate in a reaction test twice; once on a day where they drink 2 litres of water before the test and once on a day where they drink 500 ml of water before the test. The reaction times are then recorded and analysed. It is assumed that the differences in reaction times is normally distributed

Answer 14

Paired t-test

Same volunteers in two conditions (paired), normally distributed

Question 15

Previous work indicate that reactions are affected by how much fluid is consumed in the day. A sample of 15 volunteers are asked to participate in a reaction test twice; once on a day where they drink 2 litres of water before the test and once on a day where they drink 500 ml of water before the test. The reaction times are then recorded and analysed. It is assumed that the differences in reaction times is not normal, but symmetrically distributed

Answer 15

Paired Wilcoxon signed-rank

same volunteers in two conditions (paired), non-parametric, symmetrical

Question 16

Previous studies indicate that reactions are affected by how much fluid is consumed in the day. A sample of 15 volunteers are asked to participate in a reaction test twice; once on a day where they drink 2 litres of water before the test and once on a day where they drink 500 ml of water before the test. The reaction times are then recorded and analysed. No assumptions are made about the differences in reaction times

Answer 16

Paired sign test

same volunteers in two conditions (paired), non-parametric, not symmetrical

Question 17

Callum thinks an investigation should be carried out into whether there is an association between the age of a person and the amount of calories consumed. People from three age categories (20s, 30s and 40s) where asked about their diet and placed into 4 categories (low, medium, high, very high).

Answer 17

Contingency table - chi-squared

Association test; catagorised, qualitative data

Question 18

Pat presumes that the age of a person is associated with the amount of calories consumed. A sample of 15 people is taken and the age of each person and the average amount of calories they consumed was recorded. It is assumed that the underlying population follows a bivariate normal distribution.

Answer 18

Product moment correlation coefficient (PMCC)

Test for assocaition, bivariate normal data

Question 19

Sian researched if there is an association between the age of a person and the amount of alcohol consumed. A sample of 12 people is taken and the age of each person and the average amount of alcohol they consumed was recorded. It is assumed that the underlying population does not follow a bivariate normal distribution.

Answer 19

Spearman’s rank correlation coefficient

Test for association, not bivariate normal data

Question 20

Sarah researched if there is an association between the weight of a person and the amount of alcohol consumed. A sample of 17 people is taken and the weight of each person and the average amount of alcohol they consumed was recorded. No assumptions about the underlying population are made.

Answer 20

Spearman’s rank correlation coefficient

Test for association, not bivariate normal data

Question 21

General fraud charges are suspected to occur randomly, independently and at a constant average rate. In one year, the Crown Prosecution Service recorded the number of fraud charges to test this theory.

Answer 21

Goodness of fit

Suspect the condidtion of a Poisson - Is it a suitable model?

Question 22

Garden fires are suspected to be random, independent and at a constant average rate. In one year, 400 gardens are chosen and the time between fires in those gardens are recorded to test the theory.

Answer 22

Goodness of Fit

Suspect the condidtion of a Exponential - Is it a suitable model?

Question 23

Three age groups are studied to see if there is a difference in the amount of calories consumed. It is also considered that a person’s BMI may have an effect so this is also considered in the analysis.

Answer 23

Two-factor ANOVA

More than two categories for each of two factors (age and BMI)

Question 24

Pinewood Productions believe that if they spend more on television advertising, the more sales will be made. A sample of 15 days with the amount of expenditure on television advertising and the number of sales made on that day are recorded. A scatter diagram of the data shows an elliptical shape.

Answer 24

Product moment correlation coefficient

Test for association, elliptical shape suggests close to linear therefore bivariate normal

Question 25

Smooth Radio is investigating if the more spent on radio advertising, the more revenue is generated. A sample of 15 days with the amount of expenditure on radio advertising and the amount of revenue generated on that day are recorded. A scatter diagram of the data shows a rectangular shape.

Answer 25

Spearman's rank correlation coefficient ## Footnote Test for association, rectangular shape suggests NOT close to linear therefore not bivariate normal

Question 26

Samsung research if the more spent on television advertising, the more people will buy their products. A sample of 15 days with the amount of expenditure on television advertising and the number of sales made are recorded. It is assumed that the expenditure on television advertising does not follow a normal distribution.

Answer 26

Spearman's rank correlation coefficient ## Footnote Test for association, not bivariate normal data

Question 27

Bristol police publish a report claiming that the amount of knife-crime has decreased from last year’s percentage of 15%. A watchdog analyse the data to investigate whether this claim is correct.

Answer 27

One sample binomial proportion

Question 28

Seb researched if the more spent on television advertising, the more sales that are made. A sample of 15 days with the amount of expenditure on television advertising and the number of sales made on that day are recorded. It is assumed that the number of sales on a day follows a skewed distribution.

Answer 28

Spearman's rank correlation coefficient ## Footnote Test for association, not bivariate normal data

Question 29

Colgate toothpaste claims that their products have an effect on the amount of dental decay in a child’s mouth. 200 children with dental decay are tested with 4 different toothpastes (Colgate and 3 other leading brands). The children are then categorised into whether the amount of dental decay has reduced or not. A test for independence is carried out.

Answer 29

Contingency table - chi-squared

Question 30

Oral-B analyse whether their toothbrushes reduce the amount of plaque over other toothbrushes. A completely randomised design of 20 volunteers is used, where volunteers use one of 4 different toothbrushes (including Oral-B). A test to see if there is a difference in the mean amount of plaque is carried out.

Answer 30

One-factor ANOVA ## Footnote More than two categories - one factor (toothbrush)

Question 31

Two politics teachers, Marco and James, want to see which one of them is better at getting A* grades. One year, Marco gets 5 A* grades out of his 34 students, whereas James gets 7* grades out of his 43 students.

Answer 31

Two-sample binomial proportion ## Footnote Often called difference of two proportions test

Question 32

Tom thinks that there is a difference between car emissions between Volkswagen and Audi. Assuming that the car emissions are normally distributed with equal variances, he tests the car emissions of 7 Volkswagen cars and 9 Audi cars.

Answer 32

Two sample t-test ## Footnote Often called difference of two means, t - small samples with unknown population variances

Question 33

When Ryan performs in a production, he suspects that his performance is affected on whether it is a weeknight show or a weekend show. He randomly selects 5 weeknight shows and 5 weekend shows and ranks his performance for each show from 1 to 10. He then tests to see if there is a difference in the average ranks between weeknight and weekend shows

Answer 33

Wilcoxon rank sum ## Footnote Ranked performances (non-parametric) of two independent groups

Question 34

Baseball pitches for the New York Mets are believed to have improved since Ioan took over coaching duties. Before the previous coach, Jamie, was fired the percentage of “outs” was known to be 14%. Ioan’s percentage of “outs” is believed to have increased.

Answer 34

One sample binomial proportion test

Question 35

Generally, Fynn believes that the times at which yellow cards given out in a football game might follow a normal distribution. He watches all the games in a Premier League season and records the number of yellow cards given out during 10 minute intervals to test his theory.

Answer 35

Goodness of fit ## Footnote Suspects the normal is a suitable model

Question 36

To prove that Harvey’s Kebabs are worse than Nathan’s Kebabs, Luis taste-tests 50 kebab’s from Harvey’s and 50 kebab’s from Nathan’s. Luis finds that 28 of Harvey’s kebabs were nice but finds 32 of Nathan’s kebabs were nice.

Answer 36

Two sample binomial proportions ## Footnote Often known as the difference between two binomial proportions

Question 37

Prior work carried out by Zak shows that boxing technique can be improved by utilising a yoga breathing method. Zak’s investigation involved taking 5 boxers and using the breathing technique in one round and not using it in another round. He then gives a score out of 100 to judge the boxing technique. Zak assumes the differences in boxing technique scores is symmetrically distributed.

Answer 37

Paired Wilcoxon signed-rank ## Footnote Non-parametric, symmetrical - paired data

Question 38

Onyx Talisman is a craft jewellery store at a seaside resort in Norfolk. Maria is the manager of the store who believes that since a new shopping complex was built, her income has decreased. She records her takings over 5 days to test this theory. She assumes her takings are normally distributed.

Answer 38

One samplet-test ## Footnote small samplewith unknown population variance

Question 39

Previously, people have had to use “Statistical Tables” instead of a calculator to find probabilities from a Normal distribution. Archie is interested in whether if there is a negative linear correlation between people correctly using tables and people correctly using the calculator.

Answer 39

Product moment correlation coefficient ## Footnote linear correlation means the data is bivariate normal

Question 40

The Newport Car Garage think that there is a difference between car emissions between Hyundai and Fiat. They test the car emissions of 57 Hyundai cars and 49 Fiat cars, but do not believe the car emissions follow a normal distribution.

Answer 40

Two sample z-test ## Footnote Often known as the difference of two means z-test. Large sample, CLT applies

Question 41

Tabitha thinks a family-friendly video game can improve mental health. A total of 46 clinically depressed individuals were randomly assigned to either “treatment as usual” or “Super Mario Odyssey”. Participants performed a neuropsychological assessment which produced a score. The scores were then compared between the groups. It was assumed that the neuropsychological assessment scores were normally distributed.

Answer 41

Two sample t-test ## Footnote Small samples with unknown population variances

Question 42

Witek randomly assigns 46 clinically depressed individuals to either “treatment as usual” or “Super Mario Odyssey”. Participants performed a neuropsychological assessment which produced a score. The scores were then compared between the groups. It was assumed that the neuropsychological assessment scores followed a continuous uniform distribution.

Answer 42

Wilcoxon rank sum ## Footnote Independent sample, non-parametric

Question 43

Two neuropsychological assessments were carried out on 46 clinically depressed individuals, one on those who were randomly assigned “treatment as usual” and another on those who were randomly assigned “Super Mario Odyssey”. The neuropsychological assessment produced a score, which were then compared between the groups. It was assumed that the neuropsychological assessment scores were normally distributed with a common variance of 3.4.

Answer 43

Two sample z-test ## Footnote samll samples with known population variances

Question 44

Shea ranks 10 china plates in order of how old he thinks they are. Hope then carries out a test to determine if there is an association between the actual age of the plates and Shea’s order.

Answer 44

Spearman's rank correlation coefficient ## Footnote Association of ranked data

Question 45

“Pitch Perfect” is a term used by musicians to describe a singer who can sing a correct note at will. Jack takes a random sample of 20 professional singers and records, as a percentage, how close they are to pitch perfect (100% being pitch perfect) and how long they have been singing professionally for. He decides to test for a linear correlation.

Answer 45

Product moment correlation coefficient ## Footnote linear correlation

Question 46

Previous times a recruitment process assessing a candidate’s literacy and numeracy skills have been done, it has shown that candidates tend to do better on the numeracy skills than the literacy skills. Rhys records each candidate’s literacy and numeracy scores and then conducts a parametric test to test his theory.

Answer 46

Paired t-test ## Footnote Parametric test for paired data

Question 47

Previous studies of a recruitment process assessing a candidate’s literacy and numeracy skills have shown that candidates tend to do better on the numeracy skills than the literacy skills. Becky records each candidate’s literacy and numeracy scores and makes no assumptions about the differences in scores.

Answer 47

Paired sign test ## Footnote non-parametric, paired data, no assumptions

Question 48

Previous work on a recruitment process assessing a candidate’s literacy and numeracy skills have shown that candidates tend to do better on the numeracy skills than the literacy skills. Rhys records each candidate’s literacy and numeracy scores and assumes that the differences follow a U-shaped distribution.

Answer 48

Paired Wilcoxon signed rank ## Footnote non-parametric, paired data, U-shaped implies symmetrical