Quiz: Module 5 Practice Quiz Submit Quiz This Question: 1 pt |6 of 30 (6 complet
ID: 3356178 • Letter: Q
Question
Quiz: Module 5 Practice Quiz Submit Quiz This Question: 1 pt |6 of 30 (6 complete) This Quiz: 30 pts possible Question Help A safety engineer records the braking distances of two types of tires. Each randomly selected sample has 35 tires. The results of the tests are shown in the table At 0.10, can the engreer support the claim that the mean braking distance is diferent for the two types of tires? Assume the samples are randomly selected and that the samples are independent. Complete parts (a) through Type A x1 = 40 feet ,-48feet Type B x2 =42 feet 2 =4.6 feet (a) identify the claim and state Ho and Ha What is the claim? O A. The mean braking distance is different for the two types of tires. O B. The mean braking distance is the same sor the two types of tires. ° C. The mean braking distance is less for Type A tires than Type Bres. 0 D. The mean braking distance is greater for Type A tires than Type B tres. What are Ho and Ha (b) Find the critical value(s) and identfy the rejection region(s). The critical value(s) is/are Round to three decimal places as needed. Use a comma to separate answers as needed.) What is/are the rejection region(s)? 0 A z 2.81, z > _ 2.81 OC. z 2.58 G. z 2.575, zx2575 (c) Find the standardized test statistic z for 1-P2. B. OD. F. OH, z-2575 zExplanation / Answer
Solution:-
a)
A) The breaking distance is different for the two types of tires.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample z-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).
b) zcritical = + 1.645
Critical region is - 1.645 < z < 1.645
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1.124
c)
z = [ (x1 - x2) - d ] / SE
z = - 1.78
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
d) Interpret results. Reject H0, The standardised test statistics falls in the rejection region.
e) At the 90% significance level, there is sufficient evidence in to the favor of teh claim that the mean braking distance for tyre A is different from the one for the type B tires.
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