A random sample of 128 artworks involved in a recent auction of new art has been selected to study art auction price and prior exhibition. Some of the variables recorded for each artwork are listed below.

Variable Description subid Subject ID medium type of artwork exhibWeeks the number of weeks the artwork was exhibited before the auction price sale price (in thousands) ageArtistCat the age of the artists

Part 1

Research question: We wish to investigate whether the age of the artists involved in a recent auction of new art is distributed according to the table below. the age of the artists | 1 (less than 20) | 2 (21-30) | 3 (31-55) | 4 (more than 55) Percentage | 10 | 10 | 40 | 40 Please complete the following table calculating the values of A, B and C.

           | 1 (less than 20) | 2 (21-30) | 3 (31-55) | 4 (more than 55) | Total 

Observed Count | 34 | A=*** | 38 | 20 | 128
Expected Count | B=*** | 12.8 | 51.2 | 51.2 | 128
chi squared | 35.113 | 42.05 | C=*** | 19.013 | 99.579 A [integer]: Answer 1 Question 1 B [use at least 3dp]: Answer 2 Question 1

A chi-squared goodness-of-fit test is run to answer the research question. Consider the output of the test below, and answer the questions: Chi-squared test for given probabilities

data: table(var4) X-squared = 99.578, df = 3, p-value < 2.2e-16 What is the null hypothesis? Choose one among the following options: a. the age of the artists involved in a recent auction of new art is not distributed according to the given table of probabilities b. the age of the artists is associated with type of artwork c. the age of the artists involved in a recent auction of new art is distributed according to the given table of probabilities d. the age of the artists and type of artwork are independent Answer 3 Question 1

From the p-value as reported above, we can conclude that the decision of the test is: Answer 4 Question 1

What is the conclusion of the test? a. There is not enough evidence that the age of the artists involved in a recent auction of new art is distributed differently than the given table of probabilities b. There is evidence that the age of the artists involved in a recent auction of new art is distributed according to the given table of probabilities c. There is not evidence that the age of the artists and type of artwork are associated d. There is evidence that the age of the artists and type of artwork are independent e. There is evidence that the age of the artists and type of artwork are associated f. There is evidence that the age of the artists involved in a recent auction of new art is not distributed according to the given table of probabilities Answer 5 Question 1