Question

An auto manufacturer claims that the average length of time that one of its cars is owned before it requires a major repair is at least seven years. Assume that a survey of ten owners of the manufacture's cars finds that they went an average of 6 years before a major repair and the sample standard deviation for such time lengths was 1.8 years. Use the data to test the manufacture's claim at a 5% significance level.

A. Give the null hypothesis and alternative hypothesis and critical value(s) used to test this claim.

B. Give the test statistic and use this to test the manufacturer's claim at a 5% significance level and draw a conclusion based on this.

Answer 1

from the Given data, M=7, x=6, n10 o=118 years: 2-54. - 0:05 Nulle alternate hypothesis Ho: M<7 major repair is less than 7 years) H, : l>7 major repair is not less than 7 years) Degrees offereedom (dB)- (0-1) = 110-12 -192 {0:05,9) = 1833 (By using students t-distributio table) Test statisticios, te= to, (n-1) t=zM 6-7 -1.7568 olso 18/J10 = -1.7568 1) we kobserved have tobs < tcritical so, we camor Rejec Hó (-1.7568) < (1.8333) it is statistically not significant, so, we donot have sufficient evidence to support the claim, that the average length of time, that are of its cars are owned Before Yt otequires a majoor repair is at least seven years,