Question

To compare the braking distances for two types of tires, a safety engineer conducts break tests for each type. The results of the tests are given below. TypeA: x1 =55ft, s1 =5.3ft, n1 =25 TypeB: x2 =51ft, s2 =4.9ft, n2 =29 Assume the samples are independent, and that the population standard deviations are not equal. At = 0.05 , is there enough evidence to support the claim that the mean breaking distance for the Type A tires is greater than the mean breaking distance for the Type B tires? 1). [4pt] State the hypothesis and label which represents the claim: H 0 : H a : 2). [4pt] Sketch the appropriate distribution, find and label the Critical Value(s), and shade in  . 3). [4pt] Write the formula for the test statistic, including all necessary values, and give its computed value. 4). [2pt] Decision:

Answer 1

    

    

At = 0.05, the critical values are t_0.05 = 1.677

Reject H₀, if t > 1.677

The test statistic is

   

  

Since the test statistic value is greater than the critical value (2.863 > 1.677), so we should reject the null hypothesis.