Question A

Identify the most prevalent sources of sampling bias in the following scenarios:

1. A journalist would like to know how long patients are waiting at A&E at the Heath Hospital. She visits the A&E at random times during the week and asks all everyone in the waiting room how long they have been waiting for.

2. A YouTuber would like to know how to improve his videos, so he sends a link to an online poll to all his subscribers.

3. Spotify would like to know which decade has the most popular music, and so look at the number of streams of all the songs on their platform.

Question B

For the following scenarios identify the most appropriate hypothesis test and state whether it would be one-tailed or two-tailed?

1. An ornithologist would like to know if bald eagles have a wider average wingspan than hawk eagles. The wingspans of 22 bald eagles and 20 hawk eagles are measured.

2. An American president claims that American schoolchildren have an average of IQ of 133. A news company wishes to verify this claim, and measures the IQ of a sample of 200 American schoolchildren.

3. A telephone company would like to know if wireless or wired internet provides speedier connection. Wired and wireless speeds are measured for 50 devices at the same property.

4. A paediatrician would like to know if children develop the ability to click their fingers in their dominant hand quicker than the other. The age at which finger clicking is mastered in each hand is measures in a sample of 26 children.

5. A journalist is investigating unconscious bias at the BRIT awards and wants to know if red haired nominees win awards less often once nominated. All previous nominees considered, and their hair colour and outcome recorded.

6. A company would like to know if male employees reach top management more frequently than female employees. A random sample of 52 employees is taken, their gender and management level recorded.

7. A drug company would like to know if a new drug has any adverse effects on heart rate. A trial involving 38 patients is undertaken; their heart rates are recorded before and after administering the drug.

8. A botanist would like to know if yellow flowers are more likely to get black spot disease than blue ones. Colour and disease status are recorded for a sample of 105 flowers.

9. A historian would like to know if ancient Celts had the same average height as ancient Egyptians. 12 Celtic and 17 Egyptian skeletons were measured.

10. A psychologist would like to know if a course on intense speech therapy affects the vocabulary of Arabic and French speakers differently. The vocabularies of 40 speakers of each language are recorded before and after the course.

Question C

It is feared that a lake in Canada is being contaminated by a nearby factory. Eight pH samples are taken with the following results:

Environmentalists need to be 90% confident that the average pH of the lake is more acidic (lower pH) than pure water (with a pH of 7). Perform an appropriate hypothesis test.

Question D

In order to test the truth of Aesop’s fable, a group of philosophy students set up a race between 7 tortoises and 7 hares. The results are:

• 1st - Tortoise
• 2nd - Hare
• 3rd - Tortoise
• 4th - Tortoise
• 5th - Hare
• 6th - Hare
• 7th - Tortoise
• 8th - Tortoise
• 9th - Tortoise
• 10th - Hare
• 11th - Tortoise
• 12th - Hare
• 13th - Hare
• 14th - Hare

Perform a hypothesis test at the 95% confidence level to check whether slow and steady really does win the race.

Question E

The salaries of a selection of Chemistry graduates from the United Kingdom and from France are shown below:

• UK: \({£21700, £29450, £20800, £32100, £25550, £27400, £22000, £21250, £26000}\)
• France: \({€30600, €33630, €31200, €28500, €34600, €31750, €36950}\)

At the time the exchange rate was £1 = €1.21.

University administrators want to be 90% confident that French graduates and British graduates earn different mean salaries. Perform an appropriate hypothesis test.

Question F

The contingency table below shows the number of survivors and fatalities on the Titanic, by class.

Are class and survival status independent or not? Perform an appropriate hypothesis test at the 90% confidence level.

Question G

The contingency table below shows the results of a medical trial, where two treatment were used, A and B.

Are treatment and recovery independent or not? Perform an appropriate hypothesis test at the 95% confidence level.

Question H

In a study, children are given a score between 0 and 20 that corresponds to reading ability. Ten children are assessed and given an initial score. They are then given an hour session with a reading development specialist, and are assessed once again. The scores are given below:

The psychologists want to be 95% confident that the session with a reading development specialist has improved the children’s reading scores. Perform an appropriate hypothesis test.