At the annual Karaka Premier Yearling Sale top quality yearling (one-year old) thoroughbred horses are sold by auction.

Data was collected from the 2019, 2018, and 2017 sales. Below is information on some of the variables collected.

Variable

Type

Year

the year a yearling is offered for sale: 2019, 2018, 2017

When

auctioned

when the yearling is auctioned, categorised as:

- 1 (if a yearling is auctioned in the first third of the auctions)

- 2 (if a yearling is auctioned in the middle third of the auctions)

- 3 (if a yearling is auctioned in the final third of the auctions)

Sold

whether a yearling is sold, categorised as:

- yes

- passed in (if a yearling does not meet the reserve price)

- withdrawn (if a yearling is withdrawn from the auction)

Sex

the sex of a yearling:

- filly (female)

- colt (male)

Country

the country or region of the buyer of a yearling, categorised as: - Asia

- Australia

- New Zealand

- Other

State

the Australian state or territory an Australian buyer comes from:

- Australian Capital Territory

- New South Wales

- Northern Territory

- Queensland

- South Australia

- Tasmania

- Victoria

- Western Australia

Price

the selling price of a yearling (i.e. the price paid by a buyer) in $NZ

(a)For each of the scenarios 1 to 4 below:

(i)Write down the name of the variable(s), given in the table above, needed to examine the question.

(ii)For each variable in (i) write down its type (numeric or categorical).

(b)What tool(s) should you use to begin to investigate the scenarios 1 to 4 below?

Write down the scenario number 1 to 4 followed by the appropriate tool. Hint: Refer to the blue notes in Chapter 1 in the Lecture Workbook.

(c)Given that the underlying assumptions are satisfied, which form of analysis below should be used in the investigation of each of the scenarios 1 to 4 below? Write down the scenario number 1 to 4

followed by the appropriate Code A to F.

Scenario 1 Is there a difference between the proportion of fillies for sale that sell and the proportion of colts for sale that sell?

Scenario 2 Does the selling price depend on whether a yearling is a filly or a colt?

Scenario 3 Of the yearlings that sell, is there a difference between the proportion bought by New Zealand buyers and the proportion bought by Australian buyers?

Scenario 4 Is the selling price related to the year a yearling is offered for sale?

Code

Form of analysis

A

One sample t-test on a mean

B

One sample t-test on a proportion

C

One sample t-test on a mean of differences

D

Two sample t-test on a difference between two means

E

t-test on a difference between two proportions

F

One-way analysis of variance F-test