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of tires Brand 1 and Brand 2 Tread wear can vary considerably depending on the type of car and the group is trying to eliminate this effect by installing the two brands on the same cars chosen at random In particular each car has one tire of each brand on its front wheels with half of the cars chosen at random to have Brand 1 on the left front wheel and the rest to have Brand 2 there After all of the cars are driven over the standard test course for 20 000 miles the amount of tread wear in inches is recorded as shown in the table below 34 4 Car Brand 1 Brand 2 Difference Brand 1 Brand 2 Send data to calculator 1 2 5 7 0 45 0 51 0 46 0 42 0 34 0 37 0 46 0 32 8 0 37 0 25 0 30 0 23 0 38 0 41 0 48 0 17 0 08 0 26 0 16 0 19 0 04 0 04 0 02 0 15 Based on these data can the consumer group conclude at the 0 01 level of significance that the mean tread wears of the brands differ Answer this question by performing a hypothesis test regarding which is with a letter d subscript the population mean difference in tread wear for the two brands of tires Assume that this population of differences Brand 1 minus Brand 2 is normally distributed a State the null hypothesis Ho and the alternative hypothesis H HO H 0 b Determine the type of test statistic to use Type of test statistic Choose one Perform a two tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified If necessary consult a list of formulas c Find the value of the test statistic Round to three or more decimal places 0 d Find the two critical values at the 0 01 level of significance Round to three or more decimal places and e At the 0 01 level can the consumer group conclude that the mean tread wears of the brands differ OYes ONO H XI O X S 00 0 0 OSO O O P Q S 0 0 020 O O

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