Question

For the following two situations, we consider Ebay auctions of an activity tracker wristband called the Fitbit Charge. The outcome variable of interest is the total sale price of the Fitbit Charge at auction, which is the highest bid plus the shipping cost. Assume we have a dataset from a sample of 50 Fitbit Charge auctions including the following information: total Ebay sale price of the item in dollars (Price), whether the item was used or new (Condition), and length of the auction in hours (Duration). For each situation:

  (a) Determine the appropriate hypothesis test.
  (b) State the appropriate hypotheses.
  (c) Give the contextual definition of the parameter(s) about which you hypothesize.

Price	Condition	Duration
102.43	New	45
116.85	New	122
103.22	Used	40
⋮⋮	⋮⋮	⋮⋮

Situation 1: We want to test whether there is a statistically significant difference in average price between new and used Fitbit Charges sold on Ebay.

(a) Test to use for this situation:
One-sample tt-test
Two-sample tt-test
Regression
One-sample proportion test

(b) What are the null and alternative hypotheses for this test?

A. H0:μnew=μused
    HA:μnew≠μused  


B. H0:β1=122.37H0:β1=122.37
    HA:β1≠122.37  HA:β1≠122.37


C. H0:βnew=βused
    HA:βnew≠βused  


D. H0:μ=122.37
    HA:μ≠122.37  




Situation 2: We want to test whether this data provides statistically significant evidence that the average Ebay sales price of a Fitbit Charge differs from the manufacturer's suggested retail price of $122.37

(a) Test to use for this situation:
One-sample tt-test
Two-sample tt-test
Regression
One-sample proportion test

(b) What are the null and alternative hypotheses for this test?

A. H0:β1=122.37
    HA:β1≠122.37  


B. H0:b=122.37
    HA:b≠122.37  


C. H0: μ=122.37H0
    HA: μ≠122.37  


D. H0: μnew=μused
    HA: μnew≠μused

Answer 1

Situation 1: We want to test whether there is a statistically significant difference in average price between new and used Fitbit Charges sold on Ebay.

Two-sample tt-test

(b) What are the null and alternative hypotheses for this test?

A. H0:μnew=μused
    HA:μnew≠μused

Situation 2: We want to test whether this data provides statistically significant evidence that the average Ebay sales price of a Fitbit Charge differs from the manufacturer's suggested retail price of $122.37

a) Test to use for this situation:
One-sample tt-test

(b) What are the null and alternative hypotheses for this test?

C. H0: μ=122.37
    HA: μ≠122.37