A government\'s department of transportation requires tire manufacturers to prov
ID: 3180765 • Letter: A
Question
A government's department of transportation requires tire manufacturers to provide performance information on tire sidewalls to help prospective buyers make their purchasing decisions. One very important piece of information is the tread wear index, which indicates the tire's resistance to tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100. A consumer organization wants to test the actual tread wear index of a brand name of tires that claims "graded 200" on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.6 and a sample standard deviation of 21.2. Complete parts (a) and (b) below. a. Is there evidence that the population mean amount is different from a grade of 200? (Use a 0.10 level of significance.) State the null and alternative hypotheses. H_0: mu = 200 H_1: mu notequalto 200 Identify the critical value(s). The critical value(s) is(are) (Round to four decimal places as needed. Use a comma to separate answers as needed.)Explanation / Answer
Given,
X = 195.6
s = 21.2
n = 18
µ = 200
= 0.10 and this is a two tailed t test
df = n – 1 = 18 – 1 = 17
Therefore t critical values at (/2 and 1 – /2) or (0.05 and 0.95) are (+1.7396 and - 1.7396) (refer to t table for the values)
Extra:
t = (195.6 – 200)/(21.2/sqrt(18)) = -4.4/4.9969 = -0.880548
Therefore, referring to t table, p value = 0.3908