An auction website 'BidNow' might be interested in showing that buyers on its site tend to pay less than they would, for the corresponding new item on 'Tamono' website for a video game called Mario Kart for the Nintendo Wii. During early launch, Tamono sold this game for $46.99. The average sale price of the 52 BidNow auctions for Wii Mario Kart was $44.17 with a standard deviation of $4.15. Does this provide sufficient evidence accept the claim that auctions on BidNow pay less than new item cost on Tamono at 1% significance level. Support your claim with hypothesis and use critical value approach?

Please note: Provide your null and alternate hypothesis in form of equation (not as sentences). Use a t distribution. Provide the critical value on z distribution and compare with t statistic from the data. Please provide the final conclusion comparing the critical value with t statistic. Do not use p value approach. The objective is to analyse your understanding of critical value approach.