Question

The popular sport of mountain biking involves riding bikes off-road, often over very rough terrain. Trek is a leading manufacturer of mountain bikes, specially designed for durability and performance. A random sample of Trek mountain bikes was obtained and the weight (in kg) of each is given in the following table. 12.03 11.76 13.02 12.31 11.39 12.07 9.02 13.59 7.32 12.17 7.20 12.27 7.45 10.82 .67 7 (a) Assume the underlying distribution is normal. Find a 99% confidence interval for the true mean weight (in kg) of Trek mountain bikes. (Round your answers to four decimal places. ( kg (b) Suppose Trek claims to have the lightest mountain bikes on the market, with a mean weight of 10 kg. Using your answer in part (a), is there any evidence to suggest this claim is false? Justify your answer.

I need help with part a, round to 4 decimal places.

Answer 1

(a) We know, ~ t-distribution with (n-1) d.f. Here, n = 15.

C- s/ n

The 99% confidence interval of the true mean weight is:

[
1 - to.995,1-1 In vn
,
2 + +0.995,n-1-
] = [10.6727 - 1.7485, 10.6727 + 1.7485] = [8.9242, 12.4212]