Discussion:
Q: A consumer products testing group is evaluating two competing brands 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 random sample of 8 cars. 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 for20.000 miles, the amount of tread wear (in inches) is recorded, as shown in Table
Car Brand 1 Brand 2 Difference (Brand 1- Brand 2)
1 0.236 0.157 0.079
2 0.345 0,262 0.083
3 0.327 0.243 0.084
4 0.335 0.212 0.123
5 0.24 0.184 0.056
6 0.345 0.308 0.037
7 0.327 0.36 -0.033
8 0.314 0.319 -0.005
Based on these data, can the company conclude, at the level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding , the population mean difference in assembly times for the two processes. Assume that this population of differences (Brand 1 minus Brand 2) is normally distributed.
Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.
What is a null hypothesis?
What is the alternate hypothesis
The test statistic "t" is how many degrees of freedom?
What is the value of the test statistic?
The criticla value at the 0.01 level of significance?
At the 0.01 level,can the consumer group conclude that the mean tread wears of the brands differ