Aa Aa E. 4. Inferences about the slope of the population least-squares line Buyi

Question

Aa Aa E. 4. Inferences about the slope of the population least-squares line Buying an item sight unseen on the Internet requires a significant amount of trust in the seller. Consider this hypothesis: Potential buyers tend to give more scrutiny to offers posted by sellers with poor reputations compared to offers posted by sellers with neutral or good reputations. As a result, if buyers notice a surcharge (such as a shipping fee) levied by a seller with a poor reputation, then they reduce the (pre-surcharge) price they are willing to pay for the item. On the other hand, the (pre-surcharge) price they are willing to pay for an item offered by a seller with a neutral or a good reputation is not affected by a surcharge. This hypothesis was tested by Amar Cheema and described in a June 2008 paper entitled "Surcharges and Seller Reputation" published in the Journal of Consumer Research. Cheema collected data on 271 completed eBay auctions of three DVD trilogies: The Godfather, The Lord of the Rings, and Star Wars. For each auction, the winning bid, the surcharge, and the seller's eBay feedback score (a measure of seller's reputation) were recorded. Then the 271 auctions were partitioned into three samples of almost equal size based on the seller's feedback score. The following simple linear regression model was estimated for each group where y winning bid (in dollars and x shipping cost (in dollars) The following estimation results were obtained for the sample of 90 medium-reputation sellers: Estimated regression equation 33.04 0.43x Note: These results do not exactly duplicate Cheema's results but are representative of the Cheema study. Let b denote the estimate of the slope B. A different sample of eBay auctions cannot be expected to provide the same value of b as the current sample. So b is a random variable with a sampling distribution Suppose se 7.0807 is used to estimate o, the sum of the x values is x 437.6, and the sum of the squared x values is x2 2,518,13. Then the standard error for b is

Explanation / Answer

SE = sb = sqrt [ (yi - i)2 / (n - 2) ] / sqrt [ (xi - x)2 ], se = sqrt [ (yi - i)2 / (n - 2) ] = 7.0807

sqrt [ (xi - x)2 ] = sqrt(xi2 + x2 + 2xix) = sqrt(2518.13 + (437.6/271)2 - 2*437.6*(437.6/271)) = 33.2791

SE = 7.0807/33.2791 = 0.2128

DF = n - 2 = 269

t = b / SE = -0.43/0.2128 = -2.0210

p = 0.0443, reject null hypothesis, significant result

tcrit = +/- 1.9688

95% CI = -0.43 +/- 1.9688*0.2128 = (-0.8490, -0.0110)

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