Question 3

After many trials on their tyres, a company determined that the lifetime of the tread on their tyres was normally distributed with a mean of 55 thousand km.

A new production technique claims to extend the lifetime of the tyres. The company implemented this technique on 15 of their tyres and these tyres had mean lifetime of 65 thousand km and a sample variance of 250 (thousand km)².

(a) i. Calculate the critical value (t) and SE (standard error of the mean) for the new tyres, for a 95% confidence interval.

ii. Calculate the 95% confidence interval.

(b) To be more confident there is a difference, a 99% confidence interval is also checked.

1. What is the critical value, t, for a 99% confidence interval?
2. What is the 99% confidence interval?

(c) What conclusions can be drawn from the two different results? Where they differ, comment on what the differences mean. (5marks)

Can you give detail explanation of each questions, especially on question (C).