Question

An economist at Vanderbilt University devised a study to compare different types of online auctions. In one experiment he compared a Dutch auction to a first-place sealed bid auction. In the Dutch auction the item for sale starts at a very high price and is lowered gradually until someone finds the price low enough to buy. In the first-price sealed bid auction each bidder submits a single sealed bid before a particular deadline. After the deadline, the person with the highest bid wins. The researcher auctioned off collectible trading cards from the game Magic: The Gathering. He placed pairs of identical cards up for auction; one would go into Dutch auction and the other to the first-price sealed bid auction. He then looked at the difference in the prices he received on the pair. He repeated this for a total of 88 pairs.

[a] Explained why the data should be analyzed using paired samples as opposed to two independent samples.
[b] What makes a pair?
[c] What is the explanatory variable? Is it categorical or quantitative?
[d] What is the response variable? Is it categorical or quantitative?
[e] State the relevant hypotheses in words:
Null hypothesis:
Alternative hypothesis:
[f] Define the parameter of interest and give the symbol that should be assigned to it.
[g] State the relevant hypotheses in symbols (using a parameter):
Null hypothesis:
Alternative hypothesis:
[h] Assume the p-value is 0.17 (write a conclusion).

Answer 1

Explanation:

a. The data should be analyzed using paired samples because the economist made two measurements (samples) drawn from the same pair of identical cards. Each data point in one sample is uniquely paired to a data point in the second sample.

b. A pair is made up of two identical cards where one would go into Dutch auction and the other to the first-price sealed bid auction.

c. The explanatory variables are the types of online auction which are the Dutch auction and the first price sealed bid auction. The explanation variable here is categorical: the Dutch auction and the first price sealed bid auction.

d. The response variable which is also known as the outcome variable is prices for the 2 different auction for each pair of identical cards. This variable is quantitative.

e. Null Hypothesis in words: There is no difference in the prices obtained in the two different online auction.

Alternative hypothesis: There is a difference in the prices obtained in the two different online auction.

f. The parameter of interest in this case is the mean prices of pairs of identical cards for both auction and is assigned p.

g. Null hypothesis: p(dutch) = p(first-price sealed auction)

Alternative hypothesis: p(dutch) =/ p(first-price sealed auction)

h. Assuming the p-value is 0.17 at an assed standard 0.05 significance level, our conclusion would be to fail to reject the null hypothesis as 0.17 is greater than 0.05 or even 0.01 and we can conclude that, there is no statistically significant evidence to prove that there is a difference in the prices obtained in the two different online auction.