The manager of a firm that produces tyres claims that the mean lifetime of the tyres (thousand kilom

Question

The manager of a firm that produces tyres claims that the mean lifetime of the tyres (thousand kilometres) is $18.5$. He selects a random sample of $200$ tyres and the lifetimes of these tyres, $x$ (thousand kilometres) are summarised as follows: $$\sum(x - 18.5) = 75 \quad \sum(x - 18.5)^2 = 1968.04$$ Test at the $5\%$ significance level whether the manager's claim is supported by the data.[6] Explain what is meant by 'at the $5\%$ significance level' in the context of the question.[1] A new manufacturing process is developed to increase the lifetime of tyres (in thousands of kilometres). Over a period of time, it was found that the mean lifetime of tyres produced by the new process is $\mu_0$. The lifetime of tyres is known to follow a normal distribution with variance $9.5$. A random sample of $400$ tyres made by the new process is examined and found to have a mean lifetime of $20$. Find the set of values of $\mu_0$ in order that the firm may claim that the new process is effective at $1\%$ level of significance.[4]

Accepted Answer

(c)$0\leq \lambda_0 < 19.6$

2024 ACJC H1 Q13

2024 ACJC H1 Q13