Answer to Question #333765 in Statistics and Probability for bri

Question

1. A random sample of 15 fence posts from a garden centre was found to have a mean length of 1.84 m. The population standard deviation for these posts is taken to be 17cm.

(i) Use the t-distribution to find a symmetric 95% confidence interval for the mean length of such posts.

(ii) Interpret the 95% confidence interval found in part (i) above.

2. A particular brand of petrol was used in 80 randomly chosen cars of the same model and age. The petrol consumption, x miles per gallon, was obtained for each car. The results are summarized by

∑x=1896 and ∑x2=45959.

Calculate a 99% confidence interval for the mean petrol consumption of all cars of this model and age.